. . . . . . . . . . . . . . . . . . . . . "300"^^ . . . . . . . . "\uD478\uB9AC\uC5D0 \uBCC0\uD658"@ko . . . . . "\u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647"@ar . . . . . . "Transformasi Fourier, dinamakan atas Joseph Fourier, adalah sebuah yang menyatakan-kembali sebuah fungsi dalam sinusoidal, yaitu sebuah fungsi sinusoidal penjumlahan atau integral dikalikan oleh beberapa koefisien (\"amplitudo\"). Ada banyak variasi yang berhubungan-dekat dari transformasi ini tergantung jenis fungsi yang ditransformasikan. Lihat juga: Daftar transformasi yang berhubungan dengan Fourier."@in . . . . . . . . . . "1124346483"^^ . . . . . "Transformada de Fourier"@pt . . . . . . "Fourier inversion integral"@en . . . . . "Die Kollokation nach kleinsten Quadraten (nach lat. collocatio Anordnung, gemeinsame Stellung), engl. least squares collocation, ist ein kombiniertes Interpolations- und Ausgleichungs-Verfahren, bei dem im Gegensatz zur normalen Ausgleichsrechnung Daten mit sehr verschiedener Charakteristik verarbeitet werden k\u00F6nnen. Die Besonderheit dieser Anwendungen ist die Minimierung des mittleren Fehlers der verwendeten Messungen, indem alle Datenkonfigurationen durch eine Rotation des Geozentrums ineinander abgebildet werden (daher auch der Name Kol-lokation)."@de . . . "Em matem\u00E1tica, a transformada de Fourier \u00E9 uma transformada integral que expressa uma fun\u00E7\u00E3o em termos de sinusoidal. Existem diversas varia\u00E7\u00F5es diretamente relacionadas desta transformada, dependendo do tipo de fun\u00E7\u00E3o a transformar. A transformada de Fourier, ep\u00F4nimo a Jean-Baptiste Joseph Fourier, decomp\u00F5e uma fun\u00E7\u00E3o temporal (um sinal) em frequ\u00EAncias, tal como um acorde de um instrumento musical pode ser expresso como a amplitude (ou volume) das suas notas constituintes. A transformada de Fourier de uma fun\u00E7\u00E3o temporal \u00E9 uma fun\u00E7\u00E3o de valor complexo da frequ\u00EAncia, cujo valor absoluto representa a soma das frequ\u00EAncias presente na fun\u00E7\u00E3o original e cujo argumento complexo \u00E9 a fase de deslocamento da base sinusoidal naquela frequ\u00EAncia."@pt . . . . . . . . . . . . . . "Transformasi Fourier, dinamakan atas Joseph Fourier, adalah sebuah yang menyatakan-kembali sebuah fungsi dalam sinusoidal, yaitu sebuah fungsi sinusoidal penjumlahan atau integral dikalikan oleh beberapa koefisien (\"amplitudo\"). Ada banyak variasi yang berhubungan-dekat dari transformasi ini tergantung jenis fungsi yang ditransformasikan. Lihat juga: Daftar transformasi yang berhubungan dengan Fourier."@in . "\u5085\u91CC\u53F6\u53D8\u6362\uFF08\u6CD5\u8A9E\uFF1ATransformation de Fourier\uFF0C\u82F1\u8A9E\uFF1AFourier transform\uFF0C\u7F29\u5199\uFF1AFT\uFF09\u662F\u4E00\u79CD\u7EBF\u6027\u79EF\u5206\u53D8\u6362\uFF0C\u7528\u4E8E\u51FD\u6570\uFF08\u5E94\u7528\u4E0A\u79F0\u4F5C\u300C\u4FE1\u53F7\u300D\uFF09\u5728\u65F6\u57DF\u548C\u9891\u57DF\u4E4B\u95F4\u7684\u53D8\u6362\u3002\u56E0\u5176\u57FA\u672C\u601D\u60F3\u9996\u5148\u7531\u6CD5\u56FD\u5B66\u8005\u7EA6\u745F\u592B\u00B7\u5085\u91CC\u53F6\u7CFB\u7EDF\u5730\u63D0\u51FA\uFF0C\u6240\u4EE5\u4EE5\u5176\u540D\u5B57\u6765\u547D\u540D\u4EE5\u793A\u7EAA\u5FF5\u3002 \u5085\u91CC\u53F6\u53D8\u6362\u5728\u7269\u7406\u5B66\u548C\u5DE5\u7A0B\u5B66\u4E2D\u6709\u8BB8\u591A\u5E94\u7528\u3002\u5085\u91CC\u53F6\u53D8\u6362\u7684\u4F5C\u7528\u662F\u5C06\u51FD\u6570\u5206\u89E3\u4E3A\u4E0D\u540C\u7279\u5F81\u7684\u6B63\u5F26\u51FD\u6570\u7684\u548C\uFF0C\u5982\u540C\u5316\u5B66\u5206\u6790\u6765\u5206\u6790\u4E00\u4E2A\u5316\u5408\u7269\u7684\u5143\u7D20\u6210\u5206\u3002\u5BF9\u4E8E\u4E00\u4E2A\u51FD\u6570\uFF0C\u4E5F\u53EF\u5BF9\u5176\u8FDB\u884C\u5206\u6790\uFF0C\u6765\u786E\u5B9A\u7EC4\u6210\u5B83\u7684\u57FA\u672C\uFF08\u6B63\u5F26\u51FD\u6570\uFF09\u6210\u5206\u3002 \u7ECF\u8FC7\u5085\u91CC\u53F6\u53D8\u6362\u751F\u6210\u7684\u51FD\u6570 \u79F0\u4F5C\u539F\u51FD\u6570 \u7684\u5085\u91CC\u53F6\u53D8\u6362\uFF0C\u5E94\u7528\u610F\u4E49\u4E0A\u79F0\u4F5C\u9891\u8C31\u3002\u5728\u7279\u5B9A\u60C5\u6CC1\u4E0B\uFF0C\u5085\u91CC\u53F6\u53D8\u6362\u662F\u53EF\u9006\u7684\uFF0C\u5373\u5C06 \u901A\u8FC7\u9006\u53D8\u6362\u53EF\u4EE5\u5F97\u5230\u5176\u539F\u51FD\u6570 \u3002\u901A\u5E38\u60C5\u51B5\u4E0B\uFF0C \u662F\u4E00\u4E2A\u5B9E\u51FD\u6570\uFF0C\u800C \u5219\u662F\u4E00\u4E2A\u590D\u6570\u503C\u51FD\u6570\uFF0C\u5176\u51FD\u6570\u503C\u4F5C\u4E3A\u590D\u6570\u53EF\u540C\u65F6\u8868\u793A\u632F\u5E45\u548C\u76F8\u4F4D\u3002\u9AD8\u65AF\u51FD\u6570\u662F\u5085\u91CC\u53F6\u53D8\u6362\u7684\u672C\u5F81\u51FD\u6570\u3002"@zh . . "Furiera transformo"@eo . . . . . "Transformada de Fourier"@ca . . . . . "\u039C\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 \u03A6\u03BF\u03C5\u03C1\u03B9\u03AD"@el . . "\u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Fourier Transform)\u200F \u0647\u0648 \u0639\u0645\u0644\u064A\u0629 \u0631\u064A\u0627\u0636\u064A\u0629 \u062A\u0633\u062A\u062E\u062F\u0645 \u0644\u062A\u062D\u0648\u064A\u0644 \u062F\u0627\u0644\u0651\u0629 \u0631\u064A\u0627\u0636\u064A\u0629 \u0628\u0645\u062A\u063A\u064A\u0631 \u062D\u0642\u064A\u0642\u064A \u0648\u0630\u0627\u062A \u0642\u064A\u0645 \u0645\u0631\u0643\u0651\u0628\u0629 \u0625\u0644\u0649 \u062F\u0627\u0644\u0651\u0629 \u0623\u062E\u0631\u0649 \u0645\u0646 \u0646\u0641\u0633 \u0627\u0644\u0637\u0631\u0627\u0632. \u0648\u0643\u062B\u064A\u0631\u064B\u0627 \u0645\u0627 \u064A\u0637\u0644\u0642 \u0639\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u062C\u062F\u064A\u062F\u0629 \u0644\u0642\u0628 \u0627\u0644\u062A\u0645\u062B\u064A\u0644 \u0641\u064A \u0646\u0637\u0627\u0642 \u0627\u0644\u062A\u0651\u0631\u062F\u0651\u062F \u0644\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0623\u0635\u0644\u064A\u0629. \u0648\u0627\u0644\u0623\u0645\u0631 \u0634\u0628\u064A\u0647 \u0628\u062A\u062F\u0648\u064A\u0646 \u0627\u0644\u062A\u0622\u0644\u0641 \u0627\u0644\u0645\u0648\u0633\u064A\u0642\u064A \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u0646\u063A\u0645\u0627\u062A \u0627\u0644\u062A\u064A \u064A\u062A\u0643\u0648\u0646 \u0645\u0646\u0647\u0627 \u0630\u0644\u0643 \u0627\u0644\u062A\u0622\u0644\u0641. \u0639\u0645\u0644\u064A\u064B\u0627\u060C \u0641\u0625\u0646\u0651 \u0627\u0644\u062A\u062D\u0648\u064A\u0644 \u064A\u0642\u0648\u0645 \u0628\u062A\u062D\u0644\u064A\u0644 \u0627\u0644\u062F\u0627\u0644\u0651\u0629 \u0627\u0644\u0623\u0635\u0644 \u0625\u0644\u0649 \u0645\u0631\u0643\u0651\u0628\u0627\u062A\u0647\u0627 \u0645\u0646 \u0627\u0644\u0645\u0631\u0643\u0651\u0628\u0629. \u0648\u0625\u0646\u0651 \u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647 \u0645\u0627 \u0647\u0648 \u0625\u0644\u0627\u0651 \u0625\u062D\u062F\u0649 \u0627\u0644\u0623\u062F\u0648\u0627\u062A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629 \u0627\u0644\u0645\u062A\u0648\u0641\u0651\u0631\u0629 \u0641\u064A \u0636\u0645\u0646 \u0645\u062C\u0627\u0644 \u062A\u062D\u0644\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647. \u0641\u064A \u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647 \u0627\u0644\u0623\u0635\u0644\u064A\u060C \u0648\u0627\u0644\u0630\u064A \u062E\u0635\u0651\u0635\u062A \u0644\u0647 \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062D\u0629\u060C \u0641\u0625\u0646\u0651 \u0646\u0637\u0627\u0642 \u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0623\u0635\u0644\u064A\u0651\u0629 \u0648\u0646\u0637\u0627\u0642 \u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0646\u0627\u062A\u062C\u0629 \u0647\u0645\u0627 \u0646\u0637\u0627\u0642\u0627\u0646 \u0645\u0633\u062A\u0645\u0631\u0651\u0627\u0646 \u0648\u063A\u064A\u0631 \u0645\u062D\u062F\u0648\u062F\u064A\u0646. \u0642\u062F \u064A\u0633\u062A\u062E\u062F\u0645 \u0627\u0644\u0645\u0635\u0637\u0644\u062D \u062A\u062D\u0648\u064A\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647 \u0625\u0645\u0651\u0627 \u0644\u0644\u0625\u0634\u0627\u0631\u0629 \u0625\u0644\u0649 \u0627\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0651\u0629 \u0646\u0641\u0633\u0647\u0627\u060C \u0623\u0648 \u0644\u0644\u0625\u0634\u0627\u0631\u0629 \u0625\u0644\u0649 \u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0646\u0627\u062A\u062C\u0629 \u0639\u0646 \u0627\u0644\u062A\u062D\u0648\u064A\u0644 (\u0641\u0645\u062B\u0644\u0627\u064B\u060C \u062A\u0643\u0648\u0646 \u0627\u0644\u062F\u0627\u0644\u0629 \u0647\u064A \u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647 \u0644\u0644\u062F\u0627\u0644\u0629 )."@ar . "Die Fourier-Transformation (genauer die kontinuierliche Fourier-Transformation; Aussprache: [fu\u0281ie]) ist eine mathematische Methode aus dem Bereich der Fourier-Analyse, mit der aperiodische Signale in ein kontinuierliches Spektrum zerlegt werden. Die Funktion, die dieses Spektrum beschreibt, nennt man auch Fourier-Transformierte oder Spektralfunktion. Es handelt sich dabei um eine Integraltransformation, die nach dem Mathematiker Jean Baptiste Joseph Fourier benannt ist. Fourier f\u00FChrte im Jahr 1822 die Fourier-Reihe ein, die jedoch nur f\u00FCr periodische Signale definiert ist und zu einem diskreten Frequenzspektrum f\u00FChrt."@de . . . . . . . . . . . . . . . . . . . . "Transformacja Fouriera"@pl . . . "#0073CF"@en . "Fourierova transformace je integr\u00E1ln\u00ED transformace p\u0159ev\u00E1d\u011Bj\u00EDc\u00ED sign\u00E1l mezi \u010Dasov\u011B a frekven\u010Dn\u011B z\u00E1visl\u00FDm vyj\u00E1d\u0159en\u00EDm pomoc\u00ED harmonick\u00FDch sign\u00E1l\u016F, tj. funkc\u00ED a , obecn\u011B tedy funkc\u00ED komplexn\u00ED exponenci\u00E1ly. Slou\u017E\u00ED pro p\u0159evod sign\u00E1l\u016F z \u010Dasov\u00E9 oblasti do oblasti frekven\u010Dn\u00ED. Sign\u00E1l m\u016F\u017Ee b\u00FDt bu\u010F ve spojit\u00E9m \u010Di diskr\u00E9tn\u00EDm \u010Dase."@cs . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\uFF08\u30D5\u30FC\u30EA\u30A8\u3078\u3093\u304B\u3093\u3001\u82F1: Fourier transform\u3001FT\uFF09\u306F\u3001\u5B9F\u5909\u6570\u306E\u8907\u7D20\u307E\u305F\u306F\u5B9F\u6570\u5024\u95A2\u6570\u3092\u3001\u5225\u306E\u540C\u7A2E\u306E\u95A2\u6570\u306B\u5199\u3059\u5909\u63DB\u3067\u3042\u308B\u3002 \u5DE5\u5B66\u306B\u304A\u3044\u3066\u306F\u3001\u5909\u63DB\u5F8C\u306E\u95A2\u6570\u306F\u3082\u3068\u306E\u95A2\u6570\u306B\u542B\u307E\u308C\u308B\u5468\u6CE2\u6570\u3092\u8A18\u8FF0\u3057\u3066\u3044\u308B\u3068\u8003\u3048\u3001\u3057\u3070\u3057\u3070\u3082\u3068\u306E\u95A2\u6570\u306E\u5468\u6CE2\u6570\u9818\u57DF\u8868\u73FE (frequency domain representation) \u3068\u547C\u3070\u308C\u308B\u3002\u8A00\u3044\u63DB\u3048\u308C\u3070\u3001\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u306F\u95A2\u6570\u3092\u6B63\u5F26\u6CE2\u30FB\u4F59\u5F26\u6CE2\u306B\u5206\u89E3\u3059\u308B\u3068\u3082\u8A00\u3048\u308B\u3002 \u30D5\u30FC\u30EA\u30A8\u5909\u63DB (FT) \u306F\u4ED6\u306E\u591A\u304F\u306E\u6570\u5B66\u7684\u306A\u6F14\u7B97\u3068\u540C\u69D8\u306B\u30D5\u30FC\u30EA\u30A8\u89E3\u6790\u306E\u4E3B\u984C\u3092\u6210\u3059\u3002\u7279\u5225\u306E\u5834\u5408\u3068\u3057\u3066\u3001\u3082\u3068\u306E\u95A2\u6570\u3068\u305D\u306E\u5468\u6CE2\u9818\u57DF\u8868\u73FE\u304C\u9023\u7D9A\u304B\u3064\u975E\u6709\u754C\u3067\u3042\u308B\u5834\u5408\u3092\u8003\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u300C\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u300D\u3068\u3044\u3046\u8A00\u8449\u306F\u95A2\u6570\u306E\u5468\u6CE2\u6570\u9818\u57DF\u8868\u73FE\u306E\u3053\u3068\u3092\u6307\u3059\u3053\u3068\u3082\u3042\u308B\u3057\u3001\u95A2\u6570\u3092\u5468\u6CE2\u6570\u9818\u57DF\u8868\u73FE\u3078\u5199\u3059\u5909\u63DB\u306E\u904E\u7A0B\u30FB\u516C\u5F0F\u3092\u8A00\u3046\u3053\u3068\u3082\u3042\u308B\u3002\u306A\u304A\u3053\u306E\u547C\u79F0\u306F\u300119\u4E16\u7D00\u30D5\u30E9\u30F3\u30B9\u306E\u6570\u5B66\u8005\u30FB\u7269\u7406\u5B66\u8005\u3067\u6B21\u5143\u89E3\u6790\u306E\u5275\u59CB\u8005\u3068\u3055\u308C\u308B\u30B8\u30E7\u30BC\u30D5\u30FB\u30D5\u30FC\u30EA\u30A8\u306B\u7531\u6765\u3059\u308B\u3002"@ja . . . . . . . . . . "\u041F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0424\u0443\u0440'\u0454"@uk . . . . . . . . . . . . . . . . . "Phase shift.svg"@en . . "Trasformata di Fourier"@it . . "Transformacja Fouriera \u2013 pewien operator liniowy okre\u015Blany na pewnych przestrzeniach funkcyjnych, elementami kt\u00F3rych mog\u0105 by\u0107 funkcje zmiennych rzeczywistych. Opisuje ona rozk\u0142ad tych funkcji w bazie ortonormalnej funkcji trygonometrycznych \u2013 za pomoc\u0105 iloczynu skalarnego funkcji. Zosta\u0142a nazwana na cze\u015B\u0107 Jeana Baptiste\u2019a Josepha Fouriera. Wynikiem transformacji Fouriera jest funkcja nazywana transformat\u0105 Fouriera."@pl . . . . "\u041F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435"@ru . . "Transformation de Fourier"@fr . . . . . "Fouriertransform"@sv . . . . . . . . . . . . . . . . . "\u9078\u70B9\u6CD5"@ja . . . . "La transformada de Fourier, denominada as\u00ED por Joseph Fourier, es una transformaci\u00F3n matem\u00E1tica empleada para transformar se\u00F1ales entre el dominio del tiempo (o espacial) y el dominio de la frecuencia, que tiene muchas aplicaciones en la f\u00EDsica y la ingenier\u00EDa. Es reversible, siendo capaz de transformarse en cualquiera de los dominios al otro. El propio t\u00E9rmino se refiere tanto a la operaci\u00F3n de transformaci\u00F3n como a la funci\u00F3n que produce. La transformada de Fourier es una aplicaci\u00F3n que hace corresponder a una funci\u00F3n con otra funci\u00F3n definida de la manera siguiente:"@es . "\u30D5\u30FC\u30EA\u30A8\u5909\u63DB"@ja . . "In analisi matematica, la trasformata di Fourier \u00E8 una trasformata integrale, cio\u00E8 un operatore che trasforma una funzione in un'altra funzione mediante un'integrazione, sviluppata dal matematico francese Jean Baptiste Joseph Fourier nel 1822, nel suo trattato Th\u00E9orie analytique de la chaleur. Trova numerose applicazioni nella fisica e nell'ingegneria ovvero uno degli strumenti matematici maggiormente utilizzati nell'ambito delle scienze pure e applicate, permettendo di scrivere una funzione dipendente dal tempo come combinazione lineare (eventualmente continua) di funzioni di base esponenziali. La trasformata di Fourier associa a una funzione i valori dei coefficienti di questi sviluppi lineari, dandone in questo modo una rappresentazione nel dominio delle frequenze che viene spesso chiam"@it . . . . . "Fouriertransformatie"@nl . "#F5FFFA"@en . . "\u039F \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier, \u03C4\u03BF \u03CC\u03BD\u03BF\u03BC\u03AC \u03C4\u03BF\u03C5 \u03BF\u03C0\u03BF\u03AF\u03BF\u03C5 \u03C0\u03C1\u03BF\u03AE\u03BB\u03B8\u03B5 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u0396\u03BF\u03B6\u03AD\u03C6 \u03A6\u03BF\u03C5\u03C1\u03B9\u03AD, \u03B5\u03AF\u03BD\u03B1\u03B9 \u03AD\u03BD\u03B1\u03C2 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 \u03BC\u03B5 \u03C0\u03BF\u03BB\u03BB\u03AD\u03C2 \u03B5\u03C6\u03B1\u03C1\u03BC\u03BF\u03B3\u03AD\u03C2 \u03C3\u03C4\u03B7 \u03C6\u03C5\u03C3\u03B9\u03BA\u03AE \u03BA\u03B1\u03B9 \u03C4\u03B7\u03BD \u03BC\u03B7\u03C7\u03B1\u03BD\u03B9\u03BA\u03AE. \u03A0\u03BF\u03BB\u03CD \u03C3\u03C5\u03C7\u03BD\u03AC \u03BC\u03B5\u03C4\u03B1\u03C4\u03C1\u03AD\u03C0\u03B5\u03B9 \u03BC\u03B9\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AE \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03C7\u03C1\u03CC\u03BD\u03BF\u03C5, f(t), \u03C3\u03B5 \u03BC\u03B9\u03B1 \u03BD\u03AD\u03B1 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7,\u03C0\u03BF\u03C5 \u03BC\u03B5\u03C1\u03B9\u03BA\u03AD\u03C2 \u03C6\u03BF\u03C1\u03AD\u03C2 \u03C3\u03C5\u03BC\u03B2\u03BF\u03BB\u03AF\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03AE F, \u03C4\u03C9\u03BD \u03BF\u03C0\u03BF\u03AF\u03C9\u03BD \u03B7 \u03BC\u03BF\u03BD\u03AC\u03B4\u03B1 \u03BC\u03AD\u03C4\u03C1\u03B7\u03C3\u03AE\u03C2 \u03C4\u03BF\u03C5\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B7 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1 \u03BC\u03B5 \u03C4\u03B7\u03BD \u03BF\u03C0\u03BF\u03AF\u03B1 \u03B5\u03BC\u03C6\u03B1\u03BD\u03AF\u03B6\u03BF\u03C5\u03BD \u03BC\u03BF\u03BD\u03AC\u03B4\u03B5\u03C2 \u03BA\u03CD\u03BA\u03BB\u03BF\u03C5 / \u03B4\u03B5\u03C5\u03C4\u03B5\u03C1\u03CC\u03BB\u03B5\u03C0\u03C4\u03BF ( Hertz ) \u03AE \u03B1\u03BA\u03C4\u03AF\u03BD\u03B9\u03B1 \u03B1\u03BD\u03AC \u03B4\u03B5\u03C5\u03C4\u03B5\u03C1\u03CC\u03BB\u03B5\u03C0\u03C4\u03BF. \u0397 \u03BD\u03AD\u03B1 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C4\u03CC\u03C4\u03B5 \u03B3\u03BD\u03C9\u03C3\u03C4\u03AE \u03C9\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier \u03AE \u03BA\u03B1\u03B9 \u03C9\u03C2 \u03C6\u03AC\u03C3\u03BC\u03B1 \u03C3\u03C5\u03C7\u03BD\u03BF\u03C4\u03AE\u03C4\u03C9\u03BD \u03C4\u03B7\u03C2 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7\u03C2 f. \u039F \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2 \u03BC\u03B9\u03B1 \u03B1\u03BD\u03C4\u03B9\u03C3\u03C4\u03C1\u03AD\u03C8\u03B9\u03BC\u03B7 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7. \u0388\u03C4\u03C3\u03B9, \u03BC\u03B5 \u03B4\u03B5\u03B4\u03BF\u03BC\u03AD\u03BD\u03B7 \u03C4\u03B7\u03BD \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03C0\u03C1\u03BF\u03C3\u03B4\u03B9\u03BF\u03C1\u03B9\u03C3\u03C4\u03B5\u03AF \u03B7 \u03B1\u03C1\u03C7\u03B9\u03BA\u03AE \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7, f. \u039F\u03B9 f \u03BA\u03B1\u03B9 \u03B5\u03AF\u03BD\u03B1\u03B9, \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2, \u03B1\u03BD\u03C4\u03AF\u03C3\u03C4\u03BF\u03B9\u03C7\u03B1, \u03B3\u03BD\u03C9\u03C3\u03C4\u03AD\u03C2 \u03C9\u03C2 \u03C0\u03B5\u03B4\u03AF\u03BF \u03C4\u03BF\u03C5 \u03C7\u03C1\u03CC\u03BD\u03BF\u03C5 \u03BA\u03B1\u03B9 \u03C4\u03B7\u03C2 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2, \u03B1\u03BD\u03B1\u03C0\u03B1\u03C1\u03B1\u03C3\u03C4\u03AC\u03C3\u03B5\u03B9\u03C2 \u03C4\u03BF\u03C5 \u03AF\u03B4\u03B9\u03BF\u03C5 \u00AB\u03B3\u03B5\u03B3"@el . "\u039F \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier, \u03C4\u03BF \u03CC\u03BD\u03BF\u03BC\u03AC \u03C4\u03BF\u03C5 \u03BF\u03C0\u03BF\u03AF\u03BF\u03C5 \u03C0\u03C1\u03BF\u03AE\u03BB\u03B8\u03B5 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u0396\u03BF\u03B6\u03AD\u03C6 \u03A6\u03BF\u03C5\u03C1\u03B9\u03AD, \u03B5\u03AF\u03BD\u03B1\u03B9 \u03AD\u03BD\u03B1\u03C2 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 \u03BC\u03B5 \u03C0\u03BF\u03BB\u03BB\u03AD\u03C2 \u03B5\u03C6\u03B1\u03C1\u03BC\u03BF\u03B3\u03AD\u03C2 \u03C3\u03C4\u03B7 \u03C6\u03C5\u03C3\u03B9\u03BA\u03AE \u03BA\u03B1\u03B9 \u03C4\u03B7\u03BD \u03BC\u03B7\u03C7\u03B1\u03BD\u03B9\u03BA\u03AE. \u03A0\u03BF\u03BB\u03CD \u03C3\u03C5\u03C7\u03BD\u03AC \u03BC\u03B5\u03C4\u03B1\u03C4\u03C1\u03AD\u03C0\u03B5\u03B9 \u03BC\u03B9\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AE \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03C7\u03C1\u03CC\u03BD\u03BF\u03C5, f(t), \u03C3\u03B5 \u03BC\u03B9\u03B1 \u03BD\u03AD\u03B1 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7,\u03C0\u03BF\u03C5 \u03BC\u03B5\u03C1\u03B9\u03BA\u03AD\u03C2 \u03C6\u03BF\u03C1\u03AD\u03C2 \u03C3\u03C5\u03BC\u03B2\u03BF\u03BB\u03AF\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03AE F, \u03C4\u03C9\u03BD \u03BF\u03C0\u03BF\u03AF\u03C9\u03BD \u03B7 \u03BC\u03BF\u03BD\u03AC\u03B4\u03B1 \u03BC\u03AD\u03C4\u03C1\u03B7\u03C3\u03AE\u03C2 \u03C4\u03BF\u03C5\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B7 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1 \u03BC\u03B5 \u03C4\u03B7\u03BD \u03BF\u03C0\u03BF\u03AF\u03B1 \u03B5\u03BC\u03C6\u03B1\u03BD\u03AF\u03B6\u03BF\u03C5\u03BD \u03BC\u03BF\u03BD\u03AC\u03B4\u03B5\u03C2 \u03BA\u03CD\u03BA\u03BB\u03BF\u03C5 / \u03B4\u03B5\u03C5\u03C4\u03B5\u03C1\u03CC\u03BB\u03B5\u03C0\u03C4\u03BF ( Hertz ) \u03AE \u03B1\u03BA\u03C4\u03AF\u03BD\u03B9\u03B1 \u03B1\u03BD\u03AC \u03B4\u03B5\u03C5\u03C4\u03B5\u03C1\u03CC\u03BB\u03B5\u03C0\u03C4\u03BF. \u0397 \u03BD\u03AD\u03B1 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C4\u03CC\u03C4\u03B5 \u03B3\u03BD\u03C9\u03C3\u03C4\u03AE \u03C9\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier \u03AE \u03BA\u03B1\u03B9 \u03C9\u03C2 \u03C6\u03AC\u03C3\u03BC\u03B1 \u03C3\u03C5\u03C7\u03BD\u03BF\u03C4\u03AE\u03C4\u03C9\u03BD \u03C4\u03B7\u03C2 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7\u03C2 f. \u039F \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2 \u03BC\u03B9\u03B1 \u03B1\u03BD\u03C4\u03B9\u03C3\u03C4\u03C1\u03AD\u03C8\u03B9\u03BC\u03B7 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7. \u0388\u03C4\u03C3\u03B9, \u03BC\u03B5 \u03B4\u03B5\u03B4\u03BF\u03BC\u03AD\u03BD\u03B7 \u03C4\u03B7\u03BD \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03C0\u03C1\u03BF\u03C3\u03B4\u03B9\u03BF\u03C1\u03B9\u03C3\u03C4\u03B5\u03AF \u03B7 \u03B1\u03C1\u03C7\u03B9\u03BA\u03AE \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7, f. \u039F\u03B9 f \u03BA\u03B1\u03B9 \u03B5\u03AF\u03BD\u03B1\u03B9, \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2, \u03B1\u03BD\u03C4\u03AF\u03C3\u03C4\u03BF\u03B9\u03C7\u03B1, \u03B3\u03BD\u03C9\u03C3\u03C4\u03AD\u03C2 \u03C9\u03C2 \u03C0\u03B5\u03B4\u03AF\u03BF \u03C4\u03BF\u03C5 \u03C7\u03C1\u03CC\u03BD\u03BF\u03C5 \u03BA\u03B1\u03B9 \u03C4\u03B7\u03C2 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2, \u03B1\u03BD\u03B1\u03C0\u03B1\u03C1\u03B1\u03C3\u03C4\u03AC\u03C3\u03B5\u03B9\u03C2 \u03C4\u03BF\u03C5 \u03AF\u03B4\u03B9\u03BF\u03C5 \u00AB\u03B3\u03B5\u03B3\u03BF\u03BD\u03CC\u03C4\u03BF\u03C2\u00BB.\u03A4\u03B9\u03C2 \u03C0\u03B5\u03C1\u03B9\u03C3\u03C3\u03CC\u03C4\u03B5\u03C1\u03B5\u03C2 \u03C6\u03BF\u03C1\u03AD\u03C2 \u03AF\u03C3\u03C9\u03C2, \u03B7 f \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03B9\u03B1 \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03AE \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7, \u03BA\u03B1\u03B9 \u03B7 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03B9\u03B1 \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03AE \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7, \u03CC\u03C0\u03BF\u03C5 \u03AD\u03BD\u03B1\u03C2 \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CC\u03C2 \u03B1\u03C1\u03B9\u03B8\u03BC\u03CC\u03C2 \u03C0\u03B5\u03C1\u03B9\u03B3\u03C1\u03AC\u03C6\u03B5\u03B9 \u03C4\u03CC\u03C3\u03BF \u03C4\u03BF \u03C0\u03BB\u03AC\u03C4\u03BF\u03C2 \u03CC\u03C3\u03BF \u03BA\u03B1\u03B9 \u03C4\u03B7 \u03C6\u03AC\u03C3\u03B7 \u03C4\u03B7\u03C2 \u03B1\u03BD\u03C4\u03AF\u03C3\u03C4\u03BF\u03B9\u03C7\u03B7\u03C2 \u03C3\u03C5\u03BD\u03B9\u03C3\u03C4\u03CE\u03C3\u03B1\u03C2 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2. \u03A3\u03B5 \u03B3\u03B5\u03BD\u03B9\u03BA\u03AD\u03C2 \u03B3\u03C1\u03B1\u03BC\u03BC\u03AD\u03C2, \u03B7 f \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2 \u03C3\u03CD\u03BD\u03B8\u03B5\u03C4\u03B7, \u03CC\u03C0\u03C9\u03C2 \u03B7 \u03B1\u03BD\u03B1\u03BB\u03C5\u03C4\u03B9\u03BA\u03AE \u03B1\u03BD\u03B1\u03C0\u03B1\u03C1\u03AC\u03C3\u03C4\u03B1\u03C3\u03B7 \u03BC\u03B9\u03B1\u03C2 \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03AE\u03C2 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7\u03C2. \u039F \u03CC\u03C1\u03BF\u03C2 \"\u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier\" \u03B1\u03BD\u03B1\u03C6\u03AD\u03C1\u03B5\u03C4\u03B1\u03B9 \u03C4\u03CC\u03C3\u03BF \u03C3\u03C4\u03B7\u03BD \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03BF\u03CD \u03CC\u03C3\u03BF \u03BA\u03B1\u03B9 \u03C3\u03C4\u03B7\u03BD \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03AE \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03C0\u03BF\u03C5 \u03C0\u03B1\u03C1\u03AC\u03B3\u03B5\u03B9. \u03A3\u03C4\u03B7\u03BD \u03C0\u03B5\u03C1\u03AF\u03C0\u03C4\u03C9\u03C3\u03B7 \u03BC\u03B9\u03B1\u03C2 \u03C0\u03B5\u03C1\u03B9\u03BF\u03B4\u03B9\u03BA\u03AE\u03C2 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7\u03C2 (\u03B3\u03B9\u03B1 \u03C0\u03B1\u03C1\u03AC\u03B4\u03B5\u03B9\u03B3\u03BC\u03B1, \u03BC\u03B9\u03B1 \u03C3\u03C5\u03BD\u03B5\u03C7\u03AE\u03C2, \u03B1\u03BB\u03BB\u03AC \u03CC\u03C7\u03B9 \u03B1\u03C0\u03B1\u03C1\u03B1\u03AF\u03C4\u03B7\u03C4\u03B1 \u03B7\u03BC\u03B9\u03C4\u03BF\u03BD\u03BF\u03B5\u03B9\u03B4\u03BF\u03CD\u03C2 \u03BC\u03BF\u03C5\u03C3\u03B9\u03BA\u03BF\u03CD \u03AE\u03C7\u03BF\u03C5), \u03BF \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03B1\u03C0\u03BB\u03BF\u03C0\u03BF\u03B9\u03B7\u03B8\u03B5\u03AF \u03BC\u03B5 \u03C4\u03BF\u03BD \u03C5\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03C3\u03BC\u03CC \u03B5\u03BD\u03CC\u03C2 \u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03BF\u03CD \u03C3\u03CD\u03BD\u03BF\u03BB\u03BF \u03C3\u03CD\u03BD\u03B8\u03B5\u03C4\u03BF\u03C5 \u03C0\u03BB\u03AC\u03C4\u03BF\u03C5\u03C2, \u03C0\u03BF\u03C5 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03C3\u03C5\u03BD\u03C4\u03B5\u03BB\u03B5\u03C3\u03C4\u03AE\u03C2 \u03C3\u03B5\u03B9\u03C1\u03AC\u03C2 Fourier. \u0395\u03C0\u03AF\u03C3\u03B7\u03C2, \u03CC\u03C4\u03B1\u03BD \u03BC\u03B9\u03B1 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03C0\u03B5\u03B4\u03AF\u03BF\u03C5 \u03C7\u03C1\u03CC\u03BD\u03BF\u03C5 \u03BB\u03B5\u03B9\u03C4\u03BF\u03C5\u03C1\u03B3\u03AF\u03B1\u03C2 \u03C7\u03C1\u03B7\u03C3\u03B9\u03BC\u03BF\u03C0\u03BF\u03B9\u03B7\u03B8\u03B5\u03AF \u03B3\u03B9\u03B1 \u03C4\u03B7 \u03B4\u03B9\u03B5\u03C5\u03BA\u03CC\u03BB\u03C5\u03BD\u03C3\u03B7 \u03C4\u03B7\u03C2 \u03B1\u03C0\u03BF\u03B8\u03AE\u03BA\u03B5\u03C5\u03C3\u03B7\u03C2 \u03AE \u03C4\u03B7\u03C2 \u03B5\u03C0\u03B5\u03BE\u03B5\u03C1\u03B3\u03B1\u03C3\u03AF\u03B1\u03C2 \u03C4\u03BF\u03C5 \u03C5\u03C0\u03BF\u03BB\u03BF\u03B3\u03B9\u03C3\u03C4\u03AE , \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B1\u03BA\u03CC\u03BC\u03B1 \u03B4\u03C5\u03BD\u03B1\u03C4\u03CC \u03BD\u03B1 \u03B1\u03BD\u03B1\u03B4\u03B7\u03BC\u03B9\u03BF\u03C5\u03C1\u03B3\u03AE\u03C3\u03B5\u03B9 \u03BC\u03B9\u03B1 \u03AD\u03BA\u03B4\u03BF\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03B1\u03C1\u03C7\u03B9\u03BA\u03BF\u03CD \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03BF\u03CD Fourier \u03C3\u03CD\u03BC\u03C6\u03C9\u03BD\u03B1 \u03BC\u03B5 \u03C4\u03BF\u03BD \u03C4\u03CD\u03C0\u03BF \u03AC\u03B8\u03C1\u03BF\u03B9\u03C3\u03B7\u03C2 Poisson, \u03C0\u03BF\u03C5 \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B3\u03BD\u03C9\u03C3\u03C4\u03AE \u03C9\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03BF\u03CD \u03C7\u03C1\u03CC\u03BD\u03BF\u03C5 Fourier . \u03A4\u03B1 \u03B8\u03AD\u03BC\u03B1\u03C4\u03B1 \u03B1\u03C5\u03C4\u03AC \u03B5\u03BE\u03B5\u03C4\u03AC\u03B6\u03BF\u03BD\u03C4\u03B1\u03B9 \u03C3\u03B5 \u03C7\u03C9\u03C1\u03B9\u03C3\u03C4\u03AC \u03AC\u03C1\u03B8\u03C1\u03B1. \u0393\u03B9\u03B1 \u03BC\u03B9\u03B1 \u03B5\u03C0\u03B9\u03C3\u03BA\u03CC\u03C0\u03B7\u03C3\u03B7 \u03B1\u03C5\u03C4\u03CE\u03BD \u03BA\u03B1\u03B9 \u03AC\u03BB\u03BB\u03B5\u03C2 \u03C3\u03C5\u03BD\u03B1\u03C6\u03B5\u03AF\u03C2 \u03B4\u03C1\u03B1\u03C3\u03C4\u03B7\u03C1\u03B9\u03CC\u03C4\u03B7\u03C4\u03B5\u03C2, \u03B1\u03BD\u03B1\u03C4\u03C1\u03AD\u03BE\u03C4\u03B5 \u03C3\u03C4\u03B7\u03BD \u03B1\u03BD\u03AC\u03BB\u03C5\u03C3\u03B7 Fourier \u03AE \u03C3\u03C4\u03B7\u03BD \u039B\u03AF\u03C3\u03C4\u03B1 \u03C0\u03BF\u03C5 \u03C3\u03C7\u03B5\u03C4\u03AF\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03C4\u03BF\u03C5\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03BF\u03CD\u03C2 Fourier."@el . . "La transformada de Fourier descompon una funci\u00F3 temporal (un senyal) en les freq\u00FC\u00E8ncies que la constitueixen. Aquesta descomposici\u00F3 resultant \u00E9s una funci\u00F3 complexa, el valor absolut de la qual representa la quantitat de cada freq\u00FC\u00E8ncia present en la funci\u00F3 original, i l'argument complex de la qual \u00E9s el desfasament de la sinusoide b\u00E0sica en aquella freq\u00FC\u00E8ncia. Si b\u00E9 l'aplicaci\u00F3 de la transformada de Fourier no es limita nom\u00E9s a funcions temporals, el domini de la funci\u00F3 original se sol anomenar domini temporal. La transformada \u00E9s anomenada domini freq\u00FCencial. El terme transformada de Fourier fa refer\u00E8ncia tant a la representaci\u00F3 en el domini freq\u00FCencial com a l'operaci\u00F3 matem\u00E0tica que associa el domini freq\u00FCencial a una funci\u00F3 temporal. La transformada de Fourier gaudeix d'una s\u00E8rie de propietats de continu\u00EFtat que garanteixen que pot estendre's a espais de funcions majors i fins i tot a espais de distribucions temperades. A m\u00E9s, t\u00E9 una multitud d'aplicacions en moltes \u00E0rees de la ci\u00E8ncia i enginyeria: la f\u00EDsica, la teoria dels nombres, la combinat\u00F2ria, el processament de senyals (electr\u00F2nica), la teoria de la probabilitat, l'estad\u00EDstica, l'\u00F2ptica, la propagaci\u00F3 d'ones i altres \u00E0rees. La branca de la matem\u00E0tica que estudia la transformada de Fourier i les seves generalitzacions \u00E9s denominada an\u00E0lisi harm\u00F2nica."@ca . . . . "\u9078\u70B9\u6CD5\uFF08\u82F1: Collocation method\uFF09 \u3068\u306F\u3001\u6570\u5024\u89E3\u6790\u306B\u304A\u3044\u3066\u5E38\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3001\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3068\u7A4D\u5206\u65B9\u7A0B\u5F0F\u306B\u5BFE\u3057\u3066\u6570\u5024\u89E3\u3092\u4E0E\u3048\u308B\u65B9\u6CD5\u3067\u3042\u308B\u3002\u3053\u306E\u65B9\u6CD5\u306E\u30A2\u30A4\u30C7\u30A3\u30A2\u306F\u3001\u89E3\u5019\u88DC\uFF08\u901A\u5E38\u306F\u3042\u308B\u6B21\u6570\u4EE5\u4E0B\u306E\u591A\u9805\u5F0F\uFF09\u304B\u3089\u306A\u308B\u6709\u9650\u6B21\u5143\u306E\u30D9\u30AF\u30C8\u30EB\u7A7A\u9593\u3068\u5B9A\u7FA9\u57DF\u304B\u3089\u5E7E\u3064\u304B\u306E\u70B9\u3092\u5148\u306B\u9078\u3073\u3001\u305D\u308C\u3089\u306E\u70B9\u3067\u4E0E\u3048\u3089\u308C\u305F\u65B9\u7A0B\u5F0F\u3092\u6E80\u8DB3\u3059\u308B\u89E3\u3092\u89E3\u5019\u88DC\u306E\u7A7A\u9593\u304B\u3089\u9078\u629E\u3059\u308B\u3053\u3068\u3067\u3042\u308B\u3002\u305D\u306E\u3088\u3046\u306B\u9078\u3070\u308C\u305F\u70B9\u306F\u3001\u9078\u70B9\uFF08collocation points\uFF09\u3068\u547C\u3076\u3002"@ja . . "Fourierova transformace"@cs . . . . . . . . . . . . "Transformacja Fouriera \u2013 pewien operator liniowy okre\u015Blany na pewnych przestrzeniach funkcyjnych, elementami kt\u00F3rych mog\u0105 by\u0107 funkcje zmiennych rzeczywistych. Opisuje ona rozk\u0142ad tych funkcji w bazie ortonormalnej funkcji trygonometrycznych \u2013 za pomoc\u0105 iloczynu skalarnego funkcji. Zosta\u0142a nazwana na cze\u015B\u0107 Jeana Baptiste\u2019a Josepha Fouriera. Wynikiem transformacji Fouriera jest funkcja nazywana transformat\u0105 Fouriera."@pl . "La transformada de Fourier descompon una funci\u00F3 temporal (un senyal) en les freq\u00FC\u00E8ncies que la constitueixen. Aquesta descomposici\u00F3 resultant \u00E9s una funci\u00F3 complexa, el valor absolut de la qual representa la quantitat de cada freq\u00FC\u00E8ncia present en la funci\u00F3 original, i l'argument complex de la qual \u00E9s el desfasament de la sinusoide b\u00E0sica en aquella freq\u00FC\u00E8ncia. Si b\u00E9 l'aplicaci\u00F3 de la transformada de Fourier no es limita nom\u00E9s a funcions temporals, el domini de la funci\u00F3 original se sol anomenar domini temporal. La transformada \u00E9s anomenada domini freq\u00FCencial."@ca . . . . . . . "52247"^^ . . . 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"Fourierova transformace je integr\u00E1ln\u00ED transformace p\u0159ev\u00E1d\u011Bj\u00EDc\u00ED sign\u00E1l mezi \u010Dasov\u011B a frekven\u010Dn\u011B z\u00E1visl\u00FDm vyj\u00E1d\u0159en\u00EDm pomoc\u00ED harmonick\u00FDch sign\u00E1l\u016F, tj. funkc\u00ED a , obecn\u011B tedy funkc\u00ED komplexn\u00ED exponenci\u00E1ly. Slou\u017E\u00ED pro p\u0159evod sign\u00E1l\u016F z \u010Dasov\u00E9 oblasti do oblasti frekven\u010Dn\u00ED. Sign\u00E1l m\u016F\u017Ee b\u00FDt bu\u010F ve spojit\u00E9m \u010Di diskr\u00E9tn\u00EDm \u010Dase."@cs . . . . . "\"denboraren eremuko\" funtzioa izanik, ren Fourierren transformatua deritzo (Jean Baptiste Joseph Fourierren omenez) funtzioari, bezala definitzen dena. Berau funtzio integragarriarentzat definitua dagoelarik, non Transformatu honen bidez funtzioa \"maiztasun eremura\" aldatzen da denboraren eremuan argi azaltzen ez den informazioa lortzeko. transformatua funtzio jarrai eta bornatu bat da. -k betezten badu, bere alderantzizko transformatua: izango da. Bere propietateak direla eta: Fourier transformatua oso garrantzitsua da ekuazio diferentzialen soluzioak lortzeko."@eu . "La furiera transformo a\u016D transformo de Fourier, nomita honore al Joseph Fourier, estas integrala transformo , kiu esprimas funkcion per terminoj de sinusaj bazaj funkcioj, kio estas kiel sumo a\u016D integralo de sinusaj funkcioj multiplikitaj per iuj koeficientoj (\"argumentoj\"). Estas multaj proksime rilatantaj varia\u0135oj de \u0109i tiu transformo, resumitaj pli sube, dependantaj de la tipo de la transform-funkcio. Vidu anka\u016D en ."@eo . "Die Kollokation nach kleinsten Quadraten (nach lat. collocatio Anordnung, gemeinsame Stellung), engl. least squares collocation, ist ein kombiniertes Interpolations- und Ausgleichungs-Verfahren, bei dem im Gegensatz zur normalen Ausgleichsrechnung Daten mit sehr verschiedener Charakteristik verarbeitet werden k\u00F6nnen. Wer die Methode und deren Grundlagen erstmals entwickelt hat, ist noch nicht zweifelsfrei recherchiert. Am Institut f\u00FCr Maschinelle Rechentechnik der damaligen TH Dresden entwickelte 1958 im Rahmen seiner Doktorarbeit Kollokationsmethoden und habilitierte sich 1966 zu N\u00E4herungsverfahren f\u00FCr lineare Integrationsgleichungen 2. Art auf der Grundlage der Kollokation. Ab 1969 entwickelte Horst Kadner als ordentlicher Professor f\u00FCr Mathematische Kybernetik und Rechentechnik der TU Dresden L\u00F6sungsmethoden f\u00FCr eine spezielle Klasse von Integralgleichungen auf der Basis von Kollokationsmethoden. Ende der 1970er Jahre wurden diese Methoden vom Geod\u00E4ten und Mathematiker Helmut Moritz (Berlin/Graz) f\u00FCr die Zwecke der integrierten Geoidbestimmung aufgenommen, um geometrische und physikalische Daten der Erdfigur und des Erdschwerefeldes in einem Guss verarbeiten zu k\u00F6nnen. Moritz gab auch L\u00F6sungen des Kollokationsproblems und der Kovarianzmatrix in Schritten an, um bei gro\u00DFem Datenumfang die Computer-Rechenzeiten zu reduzieren. Umfangreiche Anwendungen stammen u. a. von Hans S\u00FCnkel (integrierte lokale Geoidbestimmung) und von Christian Tscherning (regionale Gravimetrie). Die erste astro-geod\u00E4tische Geoidbestimmung mittels LSC erfolgte 1982 an der TU Graz. Sie konnte die Genauigkeit des \u00F6sterreichischen Astrogeoides (durchschnittlich \u00B16 cm aus 700 Messpunkten der Lotabweichung) durch Einbeziehung eines globalen harmonischen Schweremodells (R.H.Rapp, bis 180. Ordnung) um etwa ein Viertel steigern und einen lokalen Datenfehler isolieren. Drei Jahre sp\u00E4ter konnte die Genauigkeit durch die Einbeziehung von etwa 10.000 Schwereanomalien auf \u00B14 cm erh\u00F6ht werden. Seit etwa 1990 dient die Kollokation auch als Basis f\u00FCr gro\u00DFr\u00E4umige Schwerefeld-Modellierungen unter Einschluss von Kugelfunktions-Entwicklungen der Satellitengeod\u00E4sie, u. a. in zwei Programmsystemen deutscher Hochschulen, und . Anwendungen in Nordeuropa (Tscherning & 1986\u20131993), in Italien, Spanien (Simo, & 1994) und in der T\u00FCrkei (Ayhan 1993) zeigten die Vorteile integraler Berechnungen durch Genauigkeitssteigerungen von etwa ein Drittel gegen\u00FCber Einzell\u00F6sungen. Die Besonderheit dieser Anwendungen ist die Minimierung des mittleren Fehlers der verwendeten Messungen, indem alle Datenkonfigurationen durch eine Rotation des Geozentrums ineinander abgebildet werden (daher auch der Name Kol-lokation). Die Kollokationsmethode wird mittlerweile auch in der Chemischen Thermodynamik angewendet."@de . . . . . . . . . . . . . . . "Fourier Transform"@en . . . ":"@en . . . . . . . . "\n* \uC0AC\uC778\uD30C\uC758 \uC9C4\uD3ED\uC774 \uB2E4\uC591\uD55C \uBC29\uC2DD\uC73C\uB85C \uD45C\uD604\uB418\uC5B4 \uC788\uB2E4. (1)\uC740 \uC77C\uBC18\uC801\uC778 \uCCA8\uB450\uCE58peak \uC9C4\uD3ED\uC744, (2)\uB294 \uCD5C\uB300\uCE58\uC640 \uCD5C\uC800\uCE58 \uC0AC\uC774\uC758 \uCC28\uC774\uB97C, (3)\uC740 \uC81C\uACF1\uD3C9\uADE0\uC81C\uACF1\uADFC\uC744, (4)\uB294 \uC8FC\uAE30\uB97C \uB098\uD0C0\uB0B8\uB2E4. \n* \u03B8\uB9CC\uD07C \uC704\uC0C1\uCC28\uAC00 \uC0DD\uAE34 \uBAA8\uC2B5 \uD478\uB9AC\uC5D0 \uBCC0\uD658(Fourier transform, FT)\uC740 \uC2DC\uAC04\uC774\uB098 \uACF5\uAC04\uC5D0 \uB300\uD55C \uD568\uC218\uB97C \uC2DC\uAC04 \uB610\uB294 \uACF5\uAC04 \uC8FC\uD30C\uC218 \uC131\uBD84\uC73C\uB85C \uBD84\uD574\uD558\uB294 \uBCC0\uD658\uC744 \uB9D0\uD55C\uB2E4. \uC885\uC885 \uC774 \uBCC0\uD658\uC73C\uB85C \uB098\uD0C0\uB09C \uC8FC\uD30C\uC218 \uC601\uC5ED\uC5D0\uC11C \uD568\uC218\uB97C \uD45C\uD604\uD55C \uACB0\uACFC\uBB3C\uC744 \uAC00\uB9AC\uD0A4\uB294 \uC6A9\uC5B4\uB85C\uB3C4 \uC0AC\uC6A9\uB41C\uB2E4. \uC870\uC81C\uD504 \uD478\uB9AC\uC5D0\uAC00 \uC5F4\uC804\uB3C4\uC5D0 \uB300\uD55C \uC5F0\uAD6C\uC5D0\uC11C \uC5F4 \uBC29\uC815\uC2DD\uC758 \uD574\uB97C \uAD6C\uD560 \uB54C \uCC98\uC74C \uC0AC\uC6A9\uB418\uC5C8\uB2E4. \uC2DC\uAC04\uC5D0 \uB300\uD55C \uD568\uC218\uB97C \uD478\uB9AC\uC5D0 \uBCC0\uD658\uD588\uC744 \uB54C \uC5BB\uC5B4\uC9C0\uB294 \uBCF5\uC18C\uD568\uC218\uC5D0\uC11C \uAC01 \uC8FC\uD30C\uC218\uC5D0\uC11C\uC758 \uC9C4\uD3ED\uC740 \uC6D0\uB798 \uD568\uC218\uB97C \uAD6C\uC131\uD558\uB358 \uADF8 \uC8FC\uD30C\uC218 \uC131\uBD84\uC758 \uD06C\uAE30\uB97C, \uD3B8\uAC01\uC740 \uAE30\uBCF8 \uC0AC\uC778 \uACE1\uC120\uACFC\uC758 \uC704\uC0C1\uCC28(phase offset)\uB97C \uB098\uD0C0\uB0B8\uB2E4. \uD478\uB9AC\uC5D0 \uBCC0\uD658\uB41C \uACB0\uACFC\uBB3C\uB85C\uBD80\uD130 \uD53C\uBCC0\uD658\uD568\uC218\uB97C \uBCF5\uC6D0\uD560 \uC218\uB3C4 \uC788\uB2E4. \uC774\uB97C \uC99D\uBA85\uD558\uB294 \uC815\uB9AC\uB97C \uB77C\uACE0 \uD55C\uB2E4."@ko . . . . . . . . . . . . . . . "right"@en . . . . . . . . . "6"^^ . . . . "Fourierren transformatu"@eu . "FourierTransform"@en . . . . . . . . . . . . . . . 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"Transformada de Fourier"@es . . . . . . . . . . . . . . . . . "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456, \u043C\u0435\u0301\u0442\u043E\u0434 \u043A\u043E\u043B\u043E\u043A\u0430\u0301\u0446\u0456\u0457 \u0446\u0435 \u043C\u0435\u0442\u043E\u0434 \u0447\u0438\u0441\u043B\u043E\u0432\u043E\u0433\u043E \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u044F \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u0438\u0445 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C, \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C \u0437 \u0447\u0430\u0441\u0442\u043A\u043E\u0432\u0438\u043C\u0438 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u043C\u0438 \u0442\u0430 \u0456\u043D\u0442\u0435\u0433\u0440\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C. \u0406\u0434\u0435\u044F \u043C\u0435\u0442\u043E\u0434\u0443 \u043F\u043E\u043B\u044F\u0433\u0430\u0454 \u0432 \u0442\u043E\u043C\u0443, \u0449\u043E \u043D\u0435\u043E\u0431\u0445\u0456\u0434\u043D\u043E \u0432\u0438\u0431\u0440\u0430\u0442\u0438 \u043F\u0440\u043E\u0441\u0442\u0456\u0440 \u043C\u043E\u0436\u043B\u0438\u0432\u0438\u0445 \u0440\u043E\u0437\u0432'\u044F\u0437\u043A\u0456\u0432 (\u0437\u0430\u0437\u0432\u0438\u0447\u0430\u0439 \u0446\u0435 \u043C\u043D\u043E\u0433\u043E\u0447\u043B\u0435\u043D\u0438 \u0434\u043E \u0434\u0435\u044F\u043A\u043E\u0433\u043E \u0441\u0442\u0435\u043F\u0435\u043D\u044F) \u0456 \u043A\u0456\u043B\u044C\u043A\u043E\u0441\u0442\u0456 \u0442\u043E\u0447\u043E\u043A \u0432 \u043E\u0431\u043B\u0430\u0441\u0442\u0456 (\u0442\u043E\u0447\u043A\u0438 \u043A\u043E\u043B\u043E\u043A\u0430\u0446\u0456\u0457) \u0456 \u0432\u0438\u0431\u043E\u0440\u0443 \u0440\u043E\u0437\u0432'\u044F\u0437\u043A\u0443, \u0449\u043E \u0437\u0430\u0434\u043E\u0432\u0456\u043B\u044C\u043D\u044F\u0454 \u0434\u0430\u043D\u0435 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0432 \u0442\u043E\u0447\u043A\u0430\u0445 \u043A\u043E\u043B\u043E\u043A\u0430\u0446\u0456\u0457."@uk . "Fourier transform integral"@en . "Fouriertransformen, efter Jean Baptiste Joseph Fourier, \u00E4r en transform som ofta anv\u00E4nds till att \u00F6verf\u00F6ra en funktion fr\u00E5n tidsplanet till frekvensplanet. D\u00E4r uttrycks funktionen som summan av sina sinusoidala basfunktioner, eller deltoner. En f\u00F6ruts\u00E4ttning \u00E4r att basfunktionerna \u00E4r ortogonala. Det g\u00F6r till exempel en transformering till eller fr\u00E5n frekvensplanet relativt enkel. Fouriertransformen \u00E4r definierad f\u00F6r s\u00E5v\u00E4l tidskontinuerliga som tidsdiskreta signaler. N\u00E4r den anv\u00E4nds p\u00E5 tidsbegr\u00E4nsade eller periodiska signaler ben\u00E4mns resultatet normalt Fourierserier."@sv . . . . . . . . . . . . . . . . . . "Em matem\u00E1tica, a transformada de Fourier \u00E9 uma transformada integral que expressa uma fun\u00E7\u00E3o em termos de sinusoidal. Existem diversas varia\u00E7\u00F5es diretamente relacionadas desta transformada, dependendo do tipo de fun\u00E7\u00E3o a transformar. A transformada de Fourier, ep\u00F4nimo a Jean-Baptiste Joseph Fourier, decomp\u00F5e uma fun\u00E7\u00E3o temporal (um sinal) em frequ\u00EAncias, tal como um acorde de um instrumento musical pode ser expresso como a amplitude (ou volume) das suas notas constituintes. A transformada de Fourier de uma fun\u00E7\u00E3o temporal \u00E9 uma fun\u00E7\u00E3o de valor complexo da frequ\u00EAncia, cujo valor absoluto representa a soma das frequ\u00EAncias presente na fun\u00E7\u00E3o original e cujo argumento complexo \u00E9 a fase de deslocamento da base sinusoidal naquela frequ\u00EAncia. A transformada de Fourier \u00E9 chamada de representa\u00E7\u00E3o do dom\u00EDnio da frequ\u00EAncia do sinal original. O termo transformada de Fourier refere-se a ambas representa\u00E7\u00F5es do dom\u00EDnio frequ\u00EAncia e \u00E0 opera\u00E7\u00E3o matem\u00E1tica que associa a representa\u00E7\u00E3o dom\u00EDnio frequ\u00EAncia a uma fun\u00E7\u00E3o temporal. A transformada de Fourier n\u00E3o \u00E9 limitada a fun\u00E7\u00F5es temporais, contudo para fins de conven\u00E7\u00E3o, o dom\u00EDnio original \u00E9 comumente referido como dom\u00EDnio do tempo. Para muitas fun\u00E7\u00F5es de interesse pr\u00E1tico, pode-se definir uma opera\u00E7\u00E3o de revers\u00E3o: a transformada inversa de Fourier, tamb\u00E9m chamada de s\u00EDntese de Fourier, de um dom\u00EDnio de frequ\u00EAncia combina as contribui\u00E7\u00F5es de todas as frequ\u00EAncias diferentes para a reconstitui\u00E7\u00E3o de uma fun\u00E7\u00E3o temporal original. Opera\u00E7\u00F5es lineares aplicadas em um dos dom\u00EDnios(tempo ou frequ\u00EAncia) resultam em opera\u00E7\u00F5es correspondentes no outro dom\u00EDnio, o que, em certas ocasi\u00F5es, podem ser mais f\u00E1ceis de efetuar. A opera\u00E7\u00E3o de diferencia\u00E7\u00E3o no dom\u00EDnio do tempo corresponde \u00E0 multiplica\u00E7\u00E3o na frequ\u00EAncia, o que torna mais f\u00E1cil a an\u00E1lise de equa\u00E7\u00F5es diferenciais no dom\u00EDnio da frequ\u00EAncia. Al\u00E9m disso, a convolu\u00E7\u00E3o no dom\u00EDnio temporal corresponde \u00E0 multiplica\u00E7\u00E3o ordin\u00E1ria no dom\u00EDnio da frequ\u00EAncia. Isso significa que qualquer sistema linear que n\u00E3o varia com o tempo, como um filtro aplicado a um sinal, pode ser expressado de maneira relativamente simples como uma opera\u00E7\u00E3o nas frequ\u00EAncias. Ap\u00F3s realizar a opera\u00E7\u00E3o desejada, a transforma\u00E7\u00E3o do resultado alterna para o dom\u00EDnio do tempo. A An\u00E1lise harm\u00F4nica \u00E9 o estudo sistem\u00E1tico da rela\u00E7\u00E3o entre os dom\u00EDnios de tempo e frequ\u00EAncia, incluindo os tipos de fun\u00E7\u00F5es ou opera\u00E7\u00F5es que s\u00E3o mais \"simples\" em um ou em outro, e possui liga\u00E7\u00F5es profundas a muitas \u00E1reas da matem\u00E1tica moderna."@pt . "Fourier transform"@en . . . . . . . . . . . . . . . "A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called analysis. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time."@en . . . 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"\u041F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435 (\u0441\u0438\u043C\u0432\u043E\u043B \u2131) \u2014 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044F, \u0441\u043E\u043F\u043E\u0441\u0442\u0430\u0432\u043B\u044F\u044E\u0449\u0430\u044F \u043E\u0434\u043D\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u0439 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0439 \u0434\u0440\u0443\u0433\u0443\u044E \u0444\u0443\u043D\u043A\u0446\u0438\u044E \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u0439 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0439. \u042D\u0442\u0430 \u043D\u043E\u0432\u0430\u044F \u0444\u0443\u043D\u043A\u0446\u0438\u044F \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u0435\u0442 \u043A\u043E\u044D\u0444\u0444\u0438\u0446\u0438\u0435\u043D\u0442\u044B (\u00AB\u0430\u043C\u043F\u043B\u0438\u0442\u0443\u0434\u044B\u00BB) \u043F\u0440\u0438 \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0438 \u0438\u0441\u0445\u043E\u0434\u043D\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u043D\u0430 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u0440\u043D\u044B\u0435 \u0441\u043E\u0441\u0442\u0430\u0432\u043B\u044F\u044E\u0449\u0438\u0435 \u2014 \u0433\u0430\u0440\u043C\u043E\u043D\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u043A\u043E\u043B\u0435\u0431\u0430\u043D\u0438\u044F \u0441 \u0440\u0430\u0437\u043D\u044B\u043C\u0438 \u0447\u0430\u0441\u0442\u043E\u0442\u0430\u043C\u0438."@ru . . . . . . . . . . . . "A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called analysis. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that frequency, and the argument of the complex value represents that complex sinusoid's phase offset. If a frequency is not present, the transform has a value of 0 for that frequency. The Fourier transform is not limited to functions of time, but the domain of the original function is commonly referred to as the time domain. The Fourier inversion theorem provides a synthesis process that recreates the original function from its frequency domain representation. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the . The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution (e.g., diffusion). The Fourier transform of a Gaussian function is another Gaussian function. Joseph Fourier introduced the transform in his study of heat transfer, where Gaussian functions appear as solutions of the heat equation. The Fourier transform can be formally defined as an improper Riemann integral, making it an integral transform, although this definition is not suitable for many applications requiring a more sophisticated integration theory. For example, many relatively simple applications use the Dirac delta function, which can be treated formally as if it were a function, but the justification requires a mathematically more sophisticated viewpoint. The Fourier transform can also be generalized to functions of several variables on Euclidean space, sending a function of 3-dimensional 'position space' to a function of 3-dimensional momentum (or a function of space and time to a function of 4-momentum). This idea makes the spatial Fourier transform very natural in the study of waves, as well as in quantum mechanics, where it is important to be able to represent wave solutions as functions of either position or momentum and sometimes both. In general, functions to which Fourier methods are applicable are complex-valued, and possibly vector-valued. Still further generalization is possible to functions on groups, which, besides the original Fourier transform on R or Rn (viewed as groups under addition), notably includes the discrete-time Fourier transform (DTFT, group = Z), the discrete Fourier transform (DFT, group = Z mod N) and the Fourier series or circular Fourier transform (group = S1, the unit circle \u2248 closed finite interval with endpoints identified). The latter is routinely employed to handle periodic functions. The fast Fourier transform (FFT) is an algorithm for computing the DFT."@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "\"denboraren eremuko\" funtzioa izanik, ren Fourierren transformatua deritzo (Jean Baptiste Joseph Fourierren omenez) funtzioari, bezala definitzen dena. Berau funtzio integragarriarentzat definitua dagoelarik, non Transformatu honen bidez funtzioa \"maiztasun eremura\" aldatzen da denboraren eremuan argi azaltzen ez den informazioa lortzeko. transformatua funtzio jarrai eta bornatu bat da. -k betezten badu, bere alderantzizko transformatua: izango da. Bere propietateak direla eta: Fourier transformatua oso garrantzitsua da ekuazio diferentzialen soluzioak lortzeko."@eu . "Transformasi Fourier"@in . "In analisi matematica, la trasformata di Fourier \u00E8 una trasformata integrale, cio\u00E8 un operatore che trasforma una funzione in un'altra funzione mediante un'integrazione, sviluppata dal matematico francese Jean Baptiste Joseph Fourier nel 1822, nel suo trattato Th\u00E9orie analytique de la chaleur. Trova numerose applicazioni nella fisica e nell'ingegneria ovvero uno degli strumenti matematici maggiormente utilizzati nell'ambito delle scienze pure e applicate, permettendo di scrivere una funzione dipendente dal tempo come combinazione lineare (eventualmente continua) di funzioni di base esponenziali. La trasformata di Fourier associa a una funzione i valori dei coefficienti di questi sviluppi lineari, dandone in questo modo una rappresentazione nel dominio delle frequenze che viene spesso chiamata spettro della funzione (la relazione con il concetto di spettro di un operatore pu\u00F2 essere compresa se si considera l'operatore di convoluzione con la funzione in esame). A volte si intende per trasformata di Fourier la funzione che risulta dall'applicazione di questo operatore."@it . . . "Fourier-Transformation"@de . . . . "\u5085\u91CC\u53F6\u53D8\u6362\uFF08\u6CD5\u8A9E\uFF1ATransformation de Fourier\uFF0C\u82F1\u8A9E\uFF1AFourier transform\uFF0C\u7F29\u5199\uFF1AFT\uFF09\u662F\u4E00\u79CD\u7EBF\u6027\u79EF\u5206\u53D8\u6362\uFF0C\u7528\u4E8E\u51FD\u6570\uFF08\u5E94\u7528\u4E0A\u79F0\u4F5C\u300C\u4FE1\u53F7\u300D\uFF09\u5728\u65F6\u57DF\u548C\u9891\u57DF\u4E4B\u95F4\u7684\u53D8\u6362\u3002\u56E0\u5176\u57FA\u672C\u601D\u60F3\u9996\u5148\u7531\u6CD5\u56FD\u5B66\u8005\u7EA6\u745F\u592B\u00B7\u5085\u91CC\u53F6\u7CFB\u7EDF\u5730\u63D0\u51FA\uFF0C\u6240\u4EE5\u4EE5\u5176\u540D\u5B57\u6765\u547D\u540D\u4EE5\u793A\u7EAA\u5FF5\u3002 \u5085\u91CC\u53F6\u53D8\u6362\u5728\u7269\u7406\u5B66\u548C\u5DE5\u7A0B\u5B66\u4E2D\u6709\u8BB8\u591A\u5E94\u7528\u3002\u5085\u91CC\u53F6\u53D8\u6362\u7684\u4F5C\u7528\u662F\u5C06\u51FD\u6570\u5206\u89E3\u4E3A\u4E0D\u540C\u7279\u5F81\u7684\u6B63\u5F26\u51FD\u6570\u7684\u548C\uFF0C\u5982\u540C\u5316\u5B66\u5206\u6790\u6765\u5206\u6790\u4E00\u4E2A\u5316\u5408\u7269\u7684\u5143\u7D20\u6210\u5206\u3002\u5BF9\u4E8E\u4E00\u4E2A\u51FD\u6570\uFF0C\u4E5F\u53EF\u5BF9\u5176\u8FDB\u884C\u5206\u6790\uFF0C\u6765\u786E\u5B9A\u7EC4\u6210\u5B83\u7684\u57FA\u672C\uFF08\u6B63\u5F26\u51FD\u6570\uFF09\u6210\u5206\u3002 \u7ECF\u8FC7\u5085\u91CC\u53F6\u53D8\u6362\u751F\u6210\u7684\u51FD\u6570 \u79F0\u4F5C\u539F\u51FD\u6570 \u7684\u5085\u91CC\u53F6\u53D8\u6362\uFF0C\u5E94\u7528\u610F\u4E49\u4E0A\u79F0\u4F5C\u9891\u8C31\u3002\u5728\u7279\u5B9A\u60C5\u6CC1\u4E0B\uFF0C\u5085\u91CC\u53F6\u53D8\u6362\u662F\u53EF\u9006\u7684\uFF0C\u5373\u5C06 \u901A\u8FC7\u9006\u53D8\u6362\u53EF\u4EE5\u5F97\u5230\u5176\u539F\u51FD\u6570 \u3002\u901A\u5E38\u60C5\u51B5\u4E0B\uFF0C \u662F\u4E00\u4E2A\u5B9E\u51FD\u6570\uFF0C\u800C \u5219\u662F\u4E00\u4E2A\u590D\u6570\u503C\u51FD\u6570\uFF0C\u5176\u51FD\u6570\u503C\u4F5C\u4E3A\u590D\u6570\u53EF\u540C\u65F6\u8868\u793A\u632F\u5E45\u548C\u76F8\u4F4D\u3002\u9AD8\u65AF\u51FD\u6570\u662F\u5085\u91CC\u53F6\u53D8\u6362\u7684\u672C\u5F81\u51FD\u6570\u3002"@zh . . . . . . . . . . . . . . . . "En analyse, la transformation de Fourier est une extension, pour les fonctions non p\u00E9riodiques, du d\u00E9veloppement en s\u00E9rie de Fourier des fonctions p\u00E9riodiques. La transformation de Fourier associe \u00E0 une fonction int\u00E9grable d\u00E9finie sur \u211D et \u00E0 valeurs r\u00E9elles ou complexes, une autre fonction sur \u211D appel\u00E9e transform\u00E9e de Fourier dont la variable ind\u00E9pendante peut s'interpr\u00E9ter en physique comme la fr\u00E9quence ou la pulsation. La transform\u00E9e de Fourier repr\u00E9sente une fonction par la densit\u00E9 spectrale dont elle provient, en tant que moyenne de fonctions trigonom\u00E9triques de toutes fr\u00E9quences. La th\u00E9orie de la mesure ainsi que la th\u00E9orie des distributions permettent de d\u00E9finir rigoureusement la transform\u00E9e de Fourier dans toute sa g\u00E9n\u00E9ralit\u00E9, elle joue un r\u00F4le fondamental dans l'analyse harmonique. Lorsqu'une fonction repr\u00E9sente un ph\u00E9nom\u00E8ne physique, comme l'\u00E9tat du champ \u00E9lectromagn\u00E9tique ou du champ acoustique en un point, on l'appelle signal et sa transform\u00E9e de Fourier s'appelle son spectre."@fr . . . . . "168513"^^ . . . . . . . "La transformada de Fourier, denominada as\u00ED por Joseph Fourier, es una transformaci\u00F3n matem\u00E1tica empleada para transformar se\u00F1ales entre el dominio del tiempo (o espacial) y el dominio de la frecuencia, que tiene muchas aplicaciones en la f\u00EDsica y la ingenier\u00EDa. Es reversible, siendo capaz de transformarse en cualquiera de los dominios al otro. El propio t\u00E9rmino se refiere tanto a la operaci\u00F3n de transformaci\u00F3n como a la funci\u00F3n que produce. En el caso de una funci\u00F3n peri\u00F3dica en el tiempo (por ejemplo, un sonido musical continuo pero no necesariamente sinusoidal), la transformada de Fourier se puede simplificar para el c\u00E1lculo de un conjunto discreto de amplitudes complejas, llamado coeficientes de las series de Fourier. Ellos representan el espectro de frecuencia de la se\u00F1al del dominio-tiempo original. La transformada de Fourier es una aplicaci\u00F3n que hace corresponder a una funci\u00F3n con otra funci\u00F3n definida de la manera siguiente: Donde es , es decir, tiene que ser una funci\u00F3n integrable en el sentido de la integral de Lebesgue. El factor, que acompa\u00F1a la integral en definici\u00F3n facilita el enunciado de algunos de los teoremas referentes a la transformada de Fourier. Aunque esta forma de normalizar la transformada de Fourier es la m\u00E1s com\u00FAnmente adoptada, no es universal. En la pr\u00E1ctica, las variables y suelen estar asociadas a dimensiones como el tiempo \u2014segundos\u2014 y frecuencia \u2014hercios\u2014 respectivamente, si se utiliza la f\u00F3rmula alternativa: la constante cancela las dimensiones asociadas a las variables obteniendo un exponente adimensional. La transformada de Fourier as\u00ED definida goza de una serie de propiedades de continuidad que garantizan que puede extenderse a espacios de funciones mayores e incluso a espacios de funciones generalizadas. Sus aplicaciones son muchas, en \u00E1reas de la matem\u00E1tica, ciencia e ingenier\u00EDa como la f\u00EDsica, la teor\u00EDa de los n\u00FAmeros, la combinatoria, el procesamiento de se\u00F1ales (electr\u00F3nica), la teor\u00EDa de la probabilidad, la estad\u00EDstica, la \u00F3ptica, la propagaci\u00F3n de ondas y otras \u00E1reas. En procesamiento de se\u00F1ales la transformada de Fourier suele considerarse como la descomposici\u00F3n de una se\u00F1al en componentes de frecuencias diferentes, es decir, corresponde al espectro de frecuencias de la se\u00F1al . La rama de la matem\u00E1tica que estudia la transformada de Fourier y sus generalizaciones es denominada an\u00E1lisis arm\u00F3nico."@es . "\u5085\u91CC\u53F6\u53D8\u6362"@zh . . "Die Fourier-Transformation (genauer die kontinuierliche Fourier-Transformation; Aussprache: [fu\u0281ie]) ist eine mathematische Methode aus dem Bereich der Fourier-Analyse, mit der aperiodische Signale in ein kontinuierliches Spektrum zerlegt werden. Die Funktion, die dieses Spektrum beschreibt, nennt man auch Fourier-Transformierte oder Spektralfunktion. Es handelt sich dabei um eine Integraltransformation, die nach dem Mathematiker Jean Baptiste Joseph Fourier benannt ist. Fourier f\u00FChrte im Jahr 1822 die Fourier-Reihe ein, die jedoch nur f\u00FCr periodische Signale definiert ist und zu einem diskreten Frequenzspektrum f\u00FChrt. Es gibt einige Anwendungsf\u00E4lle, in denen die Fourier-Transformation mittels eines Computers berechnet werden soll. Daf\u00FCr wurde die Diskrete Fourier-Transformation beziehungsweise die Schnelle Fourier-Transformation eingef\u00FChrt."@de . . . . . . . . . . . . . . . . . . "\u041F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435 (\u0441\u0438\u043C\u0432\u043E\u043B \u2131) \u2014 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044F, \u0441\u043E\u043F\u043E\u0441\u0442\u0430\u0432\u043B\u044F\u044E\u0449\u0430\u044F \u043E\u0434\u043D\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u0439 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0439 \u0434\u0440\u0443\u0433\u0443\u044E \u0444\u0443\u043D\u043A\u0446\u0438\u044E \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u0439 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0439. \u042D\u0442\u0430 \u043D\u043E\u0432\u0430\u044F \u0444\u0443\u043D\u043A\u0446\u0438\u044F \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u0435\u0442 \u043A\u043E\u044D\u0444\u0444\u0438\u0446\u0438\u0435\u043D\u0442\u044B (\u00AB\u0430\u043C\u043F\u043B\u0438\u0442\u0443\u0434\u044B\u00BB) \u043F\u0440\u0438 \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0438 \u0438\u0441\u0445\u043E\u0434\u043D\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u043D\u0430 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u0440\u043D\u044B\u0435 \u0441\u043E\u0441\u0442\u0430\u0432\u043B\u044F\u044E\u0449\u0438\u0435 \u2014 \u0433\u0430\u0440\u043C\u043E\u043D\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u043A\u043E\u043B\u0435\u0431\u0430\u043D\u0438\u044F \u0441 \u0440\u0430\u0437\u043D\u044B\u043C\u0438 \u0447\u0430\u0441\u0442\u043E\u0442\u0430\u043C\u0438."@ru . . . . . . . . . . . . . . "Sine voltage.svg"@en . . . "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456, \u043C\u0435\u0301\u0442\u043E\u0434 \u043A\u043E\u043B\u043E\u043A\u0430\u0301\u0446\u0456\u0457 \u0446\u0435 \u043C\u0435\u0442\u043E\u0434 \u0447\u0438\u0441\u043B\u043E\u0432\u043E\u0433\u043E \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u044F \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u0438\u0445 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C, \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C \u0437 \u0447\u0430\u0441\u0442\u043A\u043E\u0432\u0438\u043C\u0438 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u043C\u0438 \u0442\u0430 \u0456\u043D\u0442\u0435\u0433\u0440\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C. \u0406\u0434\u0435\u044F \u043C\u0435\u0442\u043E\u0434\u0443 \u043F\u043E\u043B\u044F\u0433\u0430\u0454 \u0432 \u0442\u043E\u043C\u0443, \u0449\u043E \u043D\u0435\u043E\u0431\u0445\u0456\u0434\u043D\u043E \u0432\u0438\u0431\u0440\u0430\u0442\u0438 \u043F\u0440\u043E\u0441\u0442\u0456\u0440 \u043C\u043E\u0436\u043B\u0438\u0432\u0438\u0445 \u0440\u043E\u0437\u0432'\u044F\u0437\u043A\u0456\u0432 (\u0437\u0430\u0437\u0432\u0438\u0447\u0430\u0439 \u0446\u0435 \u043C\u043D\u043E\u0433\u043E\u0447\u043B\u0435\u043D\u0438 \u0434\u043E \u0434\u0435\u044F\u043A\u043E\u0433\u043E \u0441\u0442\u0435\u043F\u0435\u043D\u044F) \u0456 \u043A\u0456\u043B\u044C\u043A\u043E\u0441\u0442\u0456 \u0442\u043E\u0447\u043E\u043A \u0432 \u043E\u0431\u043B\u0430\u0441\u0442\u0456 (\u0442\u043E\u0447\u043A\u0438 \u043A\u043E\u043B\u043E\u043A\u0430\u0446\u0456\u0457) \u0456 \u0432\u0438\u0431\u043E\u0440\u0443 \u0440\u043E\u0437\u0432'\u044F\u0437\u043A\u0443, \u0449\u043E \u0437\u0430\u0434\u043E\u0432\u0456\u043B\u044C\u043D\u044F\u0454 \u0434\u0430\u043D\u0435 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0432 \u0442\u043E\u0447\u043A\u0430\u0445 \u043A\u043E\u043B\u043E\u043A\u0430\u0446\u0456\u0457."@uk . "\u6570\u5B66\u306B\u304A\u3044\u3066\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\uFF08\u30D5\u30FC\u30EA\u30A8\u3078\u3093\u304B\u3093\u3001\u82F1: Fourier transform\u3001FT\uFF09\u306F\u3001\u5B9F\u5909\u6570\u306E\u8907\u7D20\u307E\u305F\u306F\u5B9F\u6570\u5024\u95A2\u6570\u3092\u3001\u5225\u306E\u540C\u7A2E\u306E\u95A2\u6570\u306B\u5199\u3059\u5909\u63DB\u3067\u3042\u308B\u3002 \u5DE5\u5B66\u306B\u304A\u3044\u3066\u306F\u3001\u5909\u63DB\u5F8C\u306E\u95A2\u6570\u306F\u3082\u3068\u306E\u95A2\u6570\u306B\u542B\u307E\u308C\u308B\u5468\u6CE2\u6570\u3092\u8A18\u8FF0\u3057\u3066\u3044\u308B\u3068\u8003\u3048\u3001\u3057\u3070\u3057\u3070\u3082\u3068\u306E\u95A2\u6570\u306E\u5468\u6CE2\u6570\u9818\u57DF\u8868\u73FE (frequency domain representation) \u3068\u547C\u3070\u308C\u308B\u3002\u8A00\u3044\u63DB\u3048\u308C\u3070\u3001\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u306F\u95A2\u6570\u3092\u6B63\u5F26\u6CE2\u30FB\u4F59\u5F26\u6CE2\u306B\u5206\u89E3\u3059\u308B\u3068\u3082\u8A00\u3048\u308B\u3002 \u30D5\u30FC\u30EA\u30A8\u5909\u63DB (FT) \u306F\u4ED6\u306E\u591A\u304F\u306E\u6570\u5B66\u7684\u306A\u6F14\u7B97\u3068\u540C\u69D8\u306B\u30D5\u30FC\u30EA\u30A8\u89E3\u6790\u306E\u4E3B\u984C\u3092\u6210\u3059\u3002\u7279\u5225\u306E\u5834\u5408\u3068\u3057\u3066\u3001\u3082\u3068\u306E\u95A2\u6570\u3068\u305D\u306E\u5468\u6CE2\u9818\u57DF\u8868\u73FE\u304C\u9023\u7D9A\u304B\u3064\u975E\u6709\u754C\u3067\u3042\u308B\u5834\u5408\u3092\u8003\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u300C\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u300D\u3068\u3044\u3046\u8A00\u8449\u306F\u95A2\u6570\u306E\u5468\u6CE2\u6570\u9818\u57DF\u8868\u73FE\u306E\u3053\u3068\u3092\u6307\u3059\u3053\u3068\u3082\u3042\u308B\u3057\u3001\u95A2\u6570\u3092\u5468\u6CE2\u6570\u9818\u57DF\u8868\u73FE\u3078\u5199\u3059\u5909\u63DB\u306E\u904E\u7A0B\u30FB\u516C\u5F0F\u3092\u8A00\u3046\u3053\u3068\u3082\u3042\u308B\u3002\u306A\u304A\u3053\u306E\u547C\u79F0\u306F\u300119\u4E16\u7D00\u30D5\u30E9\u30F3\u30B9\u306E\u6570\u5B66\u8005\u30FB\u7269\u7406\u5B66\u8005\u3067\u6B21\u5143\u89E3\u6790\u306E\u5275\u59CB\u8005\u3068\u3055\u308C\u308B\u30B8\u30E7\u30BC\u30D5\u30FB\u30D5\u30FC\u30EA\u30A8\u306B\u7531\u6765\u3059\u308B\u3002"@ja . . . . . . . . . . . . . "\u041C\u0435\u0442\u043E\u0434 \u043A\u043E\u043B\u043E\u043A\u0430\u0446\u0456\u0457"@uk . "Kollokation nach kleinsten Quadraten"@de . . "In de wiskunde, meer bepaald binnen de fourieranalyse, is de (continue) fouriertransformatie een lineaire integraaltransformatie die een functie ontbindt in een continu spectrum van frequenties. In de wiskundige natuurkunde kan de fouriergetransformeerde van een signaal worden gezien als dat signaal in het \"frequentiedomein\". De fouriertransformatie generaliseert voor niet-periodieke functies de fourierreeks van een periodieke functie. Een generalisatie van de fouriertransformatie is de laplacetransformatie."@nl . . . . . . . "\n* \uC0AC\uC778\uD30C\uC758 \uC9C4\uD3ED\uC774 \uB2E4\uC591\uD55C \uBC29\uC2DD\uC73C\uB85C \uD45C\uD604\uB418\uC5B4 \uC788\uB2E4. (1)\uC740 \uC77C\uBC18\uC801\uC778 \uCCA8\uB450\uCE58peak \uC9C4\uD3ED\uC744, (2)\uB294 \uCD5C\uB300\uCE58\uC640 \uCD5C\uC800\uCE58 \uC0AC\uC774\uC758 \uCC28\uC774\uB97C, (3)\uC740 \uC81C\uACF1\uD3C9\uADE0\uC81C\uACF1\uADFC\uC744, (4)\uB294 \uC8FC\uAE30\uB97C \uB098\uD0C0\uB0B8\uB2E4. \n* \u03B8\uB9CC\uD07C \uC704\uC0C1\uCC28\uAC00 \uC0DD\uAE34 \uBAA8\uC2B5 \uD478\uB9AC\uC5D0 \uBCC0\uD658(Fourier transform, FT)\uC740 \uC2DC\uAC04\uC774\uB098 \uACF5\uAC04\uC5D0 \uB300\uD55C \uD568\uC218\uB97C \uC2DC\uAC04 \uB610\uB294 \uACF5\uAC04 \uC8FC\uD30C\uC218 \uC131\uBD84\uC73C\uB85C \uBD84\uD574\uD558\uB294 \uBCC0\uD658\uC744 \uB9D0\uD55C\uB2E4. \uC885\uC885 \uC774 \uBCC0\uD658\uC73C\uB85C \uB098\uD0C0\uB09C \uC8FC\uD30C\uC218 \uC601\uC5ED\uC5D0\uC11C \uD568\uC218\uB97C \uD45C\uD604\uD55C \uACB0\uACFC\uBB3C\uC744 \uAC00\uB9AC\uD0A4\uB294 \uC6A9\uC5B4\uB85C\uB3C4 \uC0AC\uC6A9\uB41C\uB2E4. \uC870\uC81C\uD504 \uD478\uB9AC\uC5D0\uAC00 \uC5F4\uC804\uB3C4\uC5D0 \uB300\uD55C \uC5F0\uAD6C\uC5D0\uC11C \uC5F4 \uBC29\uC815\uC2DD\uC758 \uD574\uB97C \uAD6C\uD560 \uB54C \uCC98\uC74C \uC0AC\uC6A9\uB418\uC5C8\uB2E4. \uC2DC\uAC04\uC5D0 \uB300\uD55C \uD568\uC218\uB97C \uD478\uB9AC\uC5D0 \uBCC0\uD658\uD588\uC744 \uB54C \uC5BB\uC5B4\uC9C0\uB294 \uBCF5\uC18C\uD568\uC218\uC5D0\uC11C \uAC01 \uC8FC\uD30C\uC218\uC5D0\uC11C\uC758 \uC9C4\uD3ED\uC740 \uC6D0\uB798 \uD568\uC218\uB97C \uAD6C\uC131\uD558\uB358 \uADF8 \uC8FC\uD30C\uC218 \uC131\uBD84\uC758 \uD06C\uAE30\uB97C, \uD3B8\uAC01\uC740 \uAE30\uBCF8 \uC0AC\uC778 \uACE1\uC120\uACFC\uC758 \uC704\uC0C1\uCC28(phase offset)\uB97C \uB098\uD0C0\uB0B8\uB2E4. \uD478\uB9AC\uC5D0 \uBCC0\uD658\uB41C \uACB0\uACFC\uBB3C\uB85C\uBD80\uD130 \uD53C\uBCC0\uD658\uD568\uC218\uB97C \uBCF5\uC6D0\uD560 \uC218\uB3C4 \uC788\uB2E4. \uC774\uB97C \uC99D\uBA85\uD558\uB294 \uC815\uB9AC\uB97C \uB77C\uACE0 \uD55C\uB2E4. \uC6D0\uB798 \uD568\uC218\uC5D0 \uC801\uC6A9\uD560 \uC218 \uC788\uB294 \uC120\uD615 \uC5F0\uC0B0\uC740 \uC8FC\uD30C\uC218 \uC601\uC5ED\uC5D0\uB3C4 \uADF8 \uB300\uC751\uB418\uB294 \uC5F0\uC0B0\uC774 \uC874\uC7AC\uD558\uB294\uB370, \uB54C\uB54C\uB85C \uC774 \uB300\uC751\uB418\uB294 \uC120\uD615 \uC5F0\uC0B0\uC774 \uB354 \uAC04\uB2E8\uD560 \uC218\uB3C4 \uC788\uB2E4. \uC2DC\uAC04 \uC601\uC5ED\uC5D0\uC11C \uBBF8\uBD84\uC740 \uC8FC\uD30C\uC218 \uC601\uC5ED\uC5D0\uC11C\uB294 \uC8FC\uD30C\uC218\uC640\uC758 \uACF1\uC148\uC73C\uB85C \uB098\uD0C0\uB098\uAE30 \uB54C\uBB38\uC5D0 \uBBF8\uBD84\uBC29\uC815\uC2DD\uC744 \uD478\uB9AC\uC5D0 \uACF5\uAC04\uC73C\uB85C \uC62E\uACA8\uC640 \uD478\uB294 \uACBD\uC6B0\uB3C4 \uC885\uC885 \uBC1C\uC0DD\uD55C\uB2E4. \uB610 \uC2DC\uAC04 \uC601\uC5ED\uC5D0\uC11C\uC758 \uD569\uC131\uACF1\uC740 \uC8FC\uD30C\uC218 \uC601\uC5ED\uC73C\uB85C \uC62E\uACA8\uC624\uBA74 \uD3C9\uBC94\uD55C \uACF1\uC148\uACFC \uAC19\uB2E4. \uC774\uB7F0 \uACBD\uC6B0\uC5D0\uB294 \uC6D0 \uD568\uC218\uB97C \uD478\uB9AC\uC5D0 \uACF5\uAC04\uC73C\uB85C \uC62E\uACA8\uC640 \uC5EC\uAE30\uC11C \uC120\uD615\uC5F0\uC0B0\uC744 \uC801\uC6A9\uD55C \uB4A4, \uB2E4\uC2DC \uC5ED\uBCC0\uD658\uC744 \uD1B5\uD574 \uC6D0 \uD568\uC218\uB97C \uBCF5\uC6D0\uD558\uB294 \uBC29\uC2DD\uC73C\uB85C \uC5F0\uC0B0\uC744 \uB354 \uC27D\uAC8C \uC801\uC6A9\uD560 \uC218 \uC788\uB2E4. \uC774\uCC98\uB7FC \uB354 \uB2E8\uC21C\uD55C \uD568\uC218\uC640 \uC5F0\uC0B0\uC740 \uC870\uD654\uD574\uC11D\uD559 \uBD84\uC57C\uC5D0\uC11C \uCCB4\uACC4\uC801\uC73C\uB85C \uC5F0\uAD6C\uB418\uACE0 \uC788\uC73C\uBA70 \uD604\uB300 \uC218\uD559\uC5D0 \uD3ED \uB113\uAC8C \uC751\uC6A9\uB418\uACE0 \uC788\uB2E4. \uC2DC\uAC04 \uC601\uC5ED\uC5D0\uC11C\uB294 \uC881\uC740 \uC9C0\uC5ED\uC5D0\uC11C \uD45C\uD604\uB418\uB294 \uD568\uC218\uB97C \uC8FC\uD30C\uC218 \uC601\uC5ED\uC73C\uB85C \uD478\uB9AC\uC5D0 \uBCC0\uD658\uD558\uBA74 \uD568\uC218\uAC00 \uB113\uAC8C \uD37C\uC9C0\uAC8C \uB41C\uB2E4. \uC774\uB97C \uBD88\uD655\uC815\uC131 \uC6D0\uB9AC\uB77C \uD55C\uB2E4. \uADF8\uB7EC\uB098 \uAC00\uC6B0\uC2A4 \uD568\uC218\uB294 \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC744 \uD574\uB3C4 \uB611\uAC19\uC774 \uAC00\uC6B0\uC2A4 \uD568\uC218\uB85C \uB098\uD0C0\uB09C\uB2E4. \uC774 \uAC00\uC6B0\uC2A4 \uD568\uC218\uB294 \uD655\uB960 \uC774\uB860\uACFC \uD1B5\uACC4\uD559\uC5D0\uC11C \uBFD0\uB9CC \uC544\uB2C8\uB77C \uC815\uADDC \uBD84\uD3EC\uB97C \uB098\uD0C0\uB0B4\uB294 \uBB3C\uB9AC \uD604\uC0C1\uC5D0 \uB300\uD55C \uC5F0\uAD6C\uC5D0\uC11C \uB9E4\uC6B0 \uC911\uC694\uD558\uAC8C \uB2E4\uB904\uC9C4\uB2E4. \uC870\uC81C\uD504 \uD478\uB9AC\uC5D0\uAC00 \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC744 \uD1B5\uD574 \uAD6C\uD55C \uC5F4 \uBC29\uC815\uC2DD\uC758 \uD574\uAC00 \uBC14\uB85C \uAC00\uC6B0\uC2A4 \uD568\uC218\uC758 \uAF34\uC744 \uB744\uC5C8\uB2E4. \uC5C4\uBC00\uD788 \uB9D0\uD558\uC790\uBA74 \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC740 \uC77C\uC885\uC758 \uC801\uBD84 \uBCC0\uD658\uC73C\uB85C, \uB9AC\uB9CC \uC774\uC0C1\uC801\uBD84\uC774\uC5B4\uC11C \uB354 \uBCF5\uC7A1\uD55C \uC801\uBD84 \uC774\uB860\uC744 \uC694\uAD6C\uD558\uB294 \uC751\uC6A9\uBD84\uC57C\uC5D0\uC11C\uB294 \uC801\uD569\uD558\uC9C0 \uC54A\uC744 \uC218 \uC788\uB2E4. \uB300\uD45C\uC801\uC73C\uB85C \uB9CE\uC740 \uACBD\uC6B0 \uB514\uB799 \uB378\uD0C0 \uD568\uC218\uB97C \uC77C\uC885\uC758 \uD568\uC218\uB85C \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC5D0 \uC751\uC6A9\uD558\uC9C0\uB9CC, \uC218\uD559\uC801\uC73C\uB85C \uC5C4\uBC00\uD55C \uAD00\uC810\uC744 \uCDE8\uD558\uC790\uBA74 \uB354 \uC2EC\uB3C4\uC788\uB294 \uACE0\uCC30\uC774 \uD544\uC694\uD55C \uAC83\uC774\uB2E4. \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC740 \uC720\uD074\uB9AC\uB4DC \uACF5\uAC04\uC758 \uBCC0\uC218\uB4E4\uB85C \uAD6C\uC131\uB41C \uD568\uC218\uB85C \uC77C\uBC18\uD654\uD560 \uC218\uB3C4 \uC788\uB2E4. \uC989, 3\uCC28\uC6D0 \uACF5\uAC04\uC758 \uD568\uC218\uB97C 3\uCC28\uC6D0 \uACF5\uAC04\uC758 \uC6B4\uB3D9\uB7C9\uC5D0 \uB300\uD55C \uD568\uC218\uB85C \uBC14\uAFC0 \uC218\uB3C4 \uC788\uACE0, \uD639\uC740 \uACF5\uAC04\uACFC \uC2DC\uAC04\uC758 \uD568\uC218\uB97C 4\uCC28\uC6D0 \uC6B4\uB3D9\uB7C9\uC5D0 \uB300\uD55C \uD568\uC218\uB85C \uBCC0\uD658\uD560 \uC218 \uC788\uB2E4. \uC774\uAC83\uC740 \uD30C\uB3D9\uC5D0 \uB300\uD55C \uC5F0\uAD6C\uB098 \uC591\uC790\uC5ED\uD559\uC5D0\uC11C\uBFD0 \uC544\uB2C8\uB77C \uACF5\uAC04\uC774\uB098 \uC6B4\uB3D9\uB7C9 \uB610\uB294 \uB458 \uBAA8\uB450\uB97C \uD568\uC218\uB85C \uD45C\uD604\uD560 \uB54C \uD30C\uB3D9 \uACF5\uC2DD \uD45C\uD604\uC774 \uC911\uC694\uD55C \uBD84\uC57C\uC5D0\uC11C \uACF5\uAC04\uC5D0\uC11C\uC758 \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC774 \uB9E4\uC6B0 \uC790\uC5F0\uC2A4\uB7FD\uAC8C \uC0AC\uC6A9\uB418\uB3C4\uB85D \uD558\uC600\uB2E4. \uC77C\uBC18\uC801\uC73C\uB85C \uD478\uB9AC\uC5D0 \uACF5\uC2DD\uC774 \uC801\uC6A9\uAC00\uB2A5\uD55C \uD568\uC218\uB294 \uBCF5\uC18C\uC218\uC774\uBA70, \uBCA1\uD130 \uAC12\uC744 \uAC00\uC9C8 \uC218 \uC788\uB2E4. \uC9D1\uD569\uAD70\uC744 \uC774\uC6A9\uD55C \uD568\uC218\uC5D0\uC11C\uB294 \uB354 \uB9CE\uC740 \uD615\uD0DC\uAC00 \uAC00\uB2A5\uD558\uB2E4. \u211D \uB610\uB294 \u211Dn (\uB367\uC148\uC5D0 \uB2EB\uD600\uC788\uB294 \uC9D1\uD569\uAD70\uC73C\uB85C \uBCF4\uC5EC\uC9C0\uB294)\uC758 \uC6D0\uB798\uC758 \uD478\uB9AC\uC5D0 \uBCC0\uD658 \uC678\uC5D0, \uC54C\uB824\uC838 \uC788\uB4EF\uC774 \uC774\uC0B0\uC2DC\uAC04 \uD478\uB9AC\uC5D0 \uBCC0\uD658(DTFT, \uC9D1\uD569 \u2124)\uACFC \uC774\uC0B0 \uD478\uB9AC\uC5D0 \uBCC0\uD658(DFT, \uC9D1\uD569 \u2124 mod N), \uD478\uB9AC\uC5D0 \uAE09\uC218, \uC6D0\uD615 \uD478\uB9AC\uC5D0 \uBCC0\uD658(\uC9D1\uD569 S1, \uB2E8\uC704\uC6D0 = \uB05D\uC810\uC774 \uAC19\uC740 \uC720\uD55C \uD3D0\uAD6C\uAC04)\uC744 \uD3EC\uD568\uD55C\uB2E4. \uB9C8\uC9C0\uB9C9 \uAC83\uC740 \uBCF4\uD1B5 \uC8FC\uAE30\uD568\uC218\uC5D0\uC11C \uB2E4\uB8E8\uC5B4\uC9C4\uB2E4. \uACE0\uC18D \uD478\uB9AC\uC5D0 \uBCC0\uD658(Fast Fourier transform)\uC740 DFT\uB97C \uACC4\uC0B0\uD558\uAE30 \uC704\uD55C \uD558\uB098\uC758 \uC54C\uACE0\uB9AC\uC998\uC774\uB2E4."@ko . . . . . . . . . . . . . . . . . . . . . . . . . "The red sinusoid can be described by peak amplitude , peak-to-peak , RMS , and wavelength . The red and blue sinusoids have a phase difference of ."@en . . "128"^^ . . . . "\u9078\u70B9\u6CD5\uFF08\u82F1: Collocation method\uFF09 \u3068\u306F\u3001\u6570\u5024\u89E3\u6790\u306B\u304A\u3044\u3066\u5E38\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3001\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3068\u7A4D\u5206\u65B9\u7A0B\u5F0F\u306B\u5BFE\u3057\u3066\u6570\u5024\u89E3\u3092\u4E0E\u3048\u308B\u65B9\u6CD5\u3067\u3042\u308B\u3002\u3053\u306E\u65B9\u6CD5\u306E\u30A2\u30A4\u30C7\u30A3\u30A2\u306F\u3001\u89E3\u5019\u88DC\uFF08\u901A\u5E38\u306F\u3042\u308B\u6B21\u6570\u4EE5\u4E0B\u306E\u591A\u9805\u5F0F\uFF09\u304B\u3089\u306A\u308B\u6709\u9650\u6B21\u5143\u306E\u30D9\u30AF\u30C8\u30EB\u7A7A\u9593\u3068\u5B9A\u7FA9\u57DF\u304B\u3089\u5E7E\u3064\u304B\u306E\u70B9\u3092\u5148\u306B\u9078\u3073\u3001\u305D\u308C\u3089\u306E\u70B9\u3067\u4E0E\u3048\u3089\u308C\u305F\u65B9\u7A0B\u5F0F\u3092\u6E80\u8DB3\u3059\u308B\u89E3\u3092\u89E3\u5019\u88DC\u306E\u7A7A\u9593\u304B\u3089\u9078\u629E\u3059\u308B\u3053\u3068\u3067\u3042\u308B\u3002\u305D\u306E\u3088\u3046\u306B\u9078\u3070\u308C\u305F\u70B9\u306F\u3001\u9078\u70B9\uFF08collocation points\uFF09\u3068\u547C\u3076\u3002"@ja . . "Fouriertransformen, efter Jean Baptiste Joseph Fourier, \u00E4r en transform som ofta anv\u00E4nds till att \u00F6verf\u00F6ra en funktion fr\u00E5n tidsplanet till frekvensplanet. D\u00E4r uttrycks funktionen som summan av sina sinusoidala basfunktioner, eller deltoner. En f\u00F6ruts\u00E4ttning \u00E4r att basfunktionerna \u00E4r ortogonala. Det g\u00F6r till exempel en transformering till eller fr\u00E5n frekvensplanet relativt enkel. Fouriertransformen \u00E4r definierad f\u00F6r s\u00E5v\u00E4l tidskontinuerliga som tidsdiskreta signaler. N\u00E4r den anv\u00E4nds p\u00E5 tidsbegr\u00E4nsade eller periodiska signaler ben\u00E4mns resultatet normalt Fourierserier. Efter den moderna tidens datorutveckling (fr\u00E5n ca 1960) har \u00E4mnet aktualiserats d\u00E5 man kunnat tillverka signalprocessorer dedikerade till diskret fouriertransform. Behovet av effektiv programkod ledde bland annat till utveckling av snabb fouriertransform. Till\u00E4mpat i behandling av ljudsignaler \u00E4r det inte l\u00E4ngre n\u00E5gra sv\u00E5righeter att utf\u00F6ra transformerna i realtid endast med mjukvaruimplementering. Det finns inga farh\u00E5gor att metoder eller processorteknologi skulle begr\u00E4nsa framtida utveckling och applikationer."@sv . . . . . . . . . . . . . . . "The top row shows a unit pulse as a function of time and its Fourier transform as a function of frequency . The bottom row shows a delayed unit pulse as a function of time and its Fourier transform as a function of frequency . Translation in the time domain is interpreted as complex phase shifts in the frequency domain. The Fourier transform decomposes a function into eigenfunctions for the group of translations. The imaginary part of is negated because a negative sign exponent has been used in the Fourier transform, which is the default as derived from the Fourier series, but the sign does not matter for a transform that is not going to be reversed."@en . . . "In de wiskunde, meer bepaald binnen de fourieranalyse, is de (continue) fouriertransformatie een lineaire integraaltransformatie die een functie ontbindt in een continu spectrum van frequenties. In de wiskundige natuurkunde kan de fouriergetransformeerde van een signaal worden gezien als dat signaal in het \"frequentiedomein\". De fouriertransformatie generaliseert voor niet-periodieke functies de fourierreeks van een periodieke functie. Een generalisatie van de fouriertransformatie is de laplacetransformatie."@nl . . "La furiera transformo a\u016D transformo de Fourier, nomita honore al Joseph Fourier, estas integrala transformo , kiu esprimas funkcion per terminoj de sinusaj bazaj funkcioj, kio estas kiel sumo a\u016D integralo de sinusaj funkcioj multiplikitaj per iuj koeficientoj (\"argumentoj\"). Estas multaj proksime rilatantaj varia\u0135oj de \u0109i tiu transformo, resumitaj pli sube, dependantaj de la tipo de la transform-funkcio. Vidu anka\u016D en ."@eo . . . . "En analyse, la transformation de Fourier est une extension, pour les fonctions non p\u00E9riodiques, du d\u00E9veloppement en s\u00E9rie de Fourier des fonctions p\u00E9riodiques. La transformation de Fourier associe \u00E0 une fonction int\u00E9grable d\u00E9finie sur \u211D et \u00E0 valeurs r\u00E9elles ou complexes, une autre fonction sur \u211D appel\u00E9e transform\u00E9e de Fourier dont la variable ind\u00E9pendante peut s'interpr\u00E9ter en physique comme la fr\u00E9quence ou la pulsation."@fr . . . .