@prefix rdf: . @prefix dbr: . @prefix yago: . dbr:Discrete_Fourier_transform rdf:type yago:Abstraction100002137 , yago:Event100029378 , yago:Function113783816 , yago:WikicatAlgorithms , yago:Procedure101023820 , yago:Rule105846932 . @prefix owl: . dbr:Discrete_Fourier_transform rdf:type owl:Thing , yago:MathematicalRelation113783581 , yago:PsychologicalFeature100023100 , yago:Act100030358 , yago:WikicatUnitaryOperators , yago:Activity100407535 , yago:YagoPermanentlyLocatedEntity , yago:Operator113786413 , yago:Algorithm105847438 , yago:Relation100031921 . @prefix rdfs: . dbr:Discrete_Fourier_transform rdfs:label "\u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB"@ja , "Trasformata discreta di Fourier"@it , "Transformada discreta de Fourier"@ca , "Diskret fouriertransform"@sv , "\u0394\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03CC\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 \u03A6\u03BF\u03C5\u03C1\u03B9\u03AD"@el , "\uC774\uC0B0 \uD478\uB9AC\uC5D0 \uBCC0\uD658"@ko , "Dyskretna transformata Fouriera"@pl , "Discrete Fourier transform"@en , "Transformation de Fourier discr\u00E8te"@fr , "Diskrete Fourier-Transformation"@de , "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0435 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0424\u0443\u0440'\u0454"@uk , "\u79BB\u6563\u5085\u91CC\u53F6\u53D8\u6362"@zh , "Transformada discreta de Fourier"@pt , "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435"@ru , "Transformasi Fourier diskrit"@in , "Discrete fouriertransformatie"@nl , "Transformada de Fourier discreta"@es , "\u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647 \u0627\u0644\u0645\u062A\u0642\u0637\u0639"@ar ; rdfs:comment "\uC774\uC0B0 \uD478\uB9AC\uC5D0 \uBCC0\uD658(discrete Fourier transform, DFT)\uC740 \uC774\uC0B0\uC801\uC778 \uC785\uB825 \uC2E0\uD638\uC5D0 \uB300\uD55C \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC73C\uB85C, \uB514\uC9C0\uD138 \uC2E0\uD638 \uBD84\uC11D\uACFC \uAC19\uC740 \uBD84\uC57C\uC5D0 \uC0AC\uC6A9\uB41C\uB2E4. \uC774\uC0B0 \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC740 \uACE0\uC18D \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC744 \uC774\uC6A9\uD574 \uBE60\uB974\uAC8C \uACC4\uC0B0\uD560 \uC218 \uC788\uB2E4."@ko , "\u03A3\u03C4\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC, \u03BF \u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03CC\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier (DFT) \u03BC\u03B5\u03C4\u03B1\u03C4\u03C1\u03AD\u03C0\u03B5\u03B9 \u03BC\u03B9\u03B1 \u03C0\u03B5\u03C0\u03B5\u03C1\u03B1\u03C3\u03BC\u03AD\u03BD\u03B7 \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03AF\u03B1 \u03B1\u03C0\u03CC \u03AF\u03C3\u03B1 \u03B4\u03B9\u03B1\u03C3\u03C4\u03AE\u03BC\u03B1\u03C4\u03B1 \u03B4\u03B5\u03B9\u03B3\u03BC\u03AC\u03C4\u03C9\u03BD \u03B1\u03C0\u03CC \u03BC\u03B9\u03B1 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03C3\u03B5 \u03BC\u03AF\u03B1 \u03BB\u03AF\u03C3\u03C4\u03B1 \u03BC\u03B5 \u03C3\u03C5\u03BD\u03C4\u03B5\u03BB\u03B5\u03C3\u03C4\u03AD\u03C2 \u03B1\u03C0\u03CC \u03AD\u03BD\u03B1 \u03C0\u03B5\u03C0\u03B5\u03C1\u03B1\u03C3\u03BC\u03AD\u03BD\u03BF \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03BC\u03CC \u03B7\u03BC\u03B9\u03C4\u03BF\u03BD\u03BF\u03B5\u03B9\u03B4\u03CE\u03BD \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CE\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD, \u03BA\u03B1\u03B8\u03BF\u03C1\u03B9\u03C3\u03BC\u03AD\u03BD\u03C9\u03BD \u03B1\u03C0\u03CC \u03C4\u03B9\u03C2 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B5\u03C2 \u03C4\u03BF\u03C5\u03C2, \u03C0\u03BF\u03C5 \u03AD\u03C7\u03B5\u03B9 \u03C4\u03B9\u03C2 \u03AF\u03B4\u03B9\u03B5\u03C2 \u03C4\u03B9\u03BC\u03AD\u03C2 \u03B4\u03B5\u03AF\u03B3\u03BC\u03B1\u03C4\u03BF\u03C2. \u0391\u03C5\u03C4\u03CC \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03B5\u03B9\u03C0\u03C9\u03B8\u03B5\u03AF \u03B3\u03B9\u03B1 \u03C4\u03B7 \u03BC\u03B5\u03C4\u03B1\u03C4\u03C1\u03BF\u03C0\u03AE \u03C4\u03BF\u03C5 \u03B4\u03B5\u03AF\u03B3\u03BC\u03B1\u03C4\u03BF\u03C2 \u03C4\u03B7\u03C2 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7\u03C2 \u03B1\u03C0\u03CC \u03C4\u03BF \u03B1\u03C1\u03C7\u03B9\u03BA\u03CC \u03C4\u03BF\u03C5 \u03C0\u03B5\u03B4\u03AF\u03BF \u03BF\u03C1\u03B9\u03C3\u03BC\u03BF\u03CD (\u03C3\u03C5\u03C7\u03BD\u03AC \u03C4\u03BF \u03C7\u03C1\u03CC\u03BD\u03BF \u03AE \u03C4\u03B7 \u03B8\u03AD\u03C3\u03B7 \u03BA\u03B1\u03C4\u03AC \u03BC\u03AE\u03BA\u03BF\u03C2 \u03C4\u03B7\u03C2 \u03B3\u03C1\u03B1\u03BC\u03BC\u03AE\u03C2) \u03C3\u03C4\u03BF \u03C0\u03B5\u03B4\u03AF\u03BF \u03C4\u03B7\u03C2 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2."@el , "In matematica, in particolare nell'analisi di Fourier, la trasformata discreta di Fourier, anche detta DFT (acronimo del termine inglese Discrete Fourier Transform), \u00E8 un particolare tipo di trasformata di Fourier. Si tratta anche di un caso particolare della trasformata zeta. Si differenzia dalla trasformata di Fourier a tempo discreto per il fatto che la funzione in ingresso e la funzione prodotta sono successioni finite, e pu\u00F2 essere quindi considerata come una trasformata per l'analisi di Fourier di funzioni su un dominio limitato e discreto."@it , "\u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A\u0647 \u0627\u0644\u0645\u062A\u0642\u0637\u0639 \u0647\u064A \u0639\u0645\u0644\u064A\u0629 \u062A\u062D\u0648\u064A\u0644 \u062A\u0645\u0643\u0646\u0646\u0627 \u062A\u062D\u0648\u064A\u0644 \u0625\u0634\u0627\u0631\u0629 \u0645\u062A\u0642\u0637\u0639\u0629 \u0641\u064A \u0641\u0636\u0627\u0621 \u0627\u0644\u0632\u0645\u0646 \u0625\u0644\u0649 \u0625\u0634\u0627\u0631\u0629 \u0641\u064A \u0641\u0636\u0627\u0621 \u0627\u0644\u062A\u0631\u062F\u062F\u0627\u062A \u0648\u0647\u064A \u0634\u0628\u064A\u0647\u0629 \u0648\u0645\u0633\u062A\u0642\u0627\u0629 \u0645\u0646 \u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A \u0627\u0644\u0630\u064A \u064A\u0642\u0648\u0645 \u0628\u062A\u062D\u0648\u064A\u0644 \u0625\u0634\u0627\u0631\u0629 (\u064A\u0645\u0643\u0646 \u0641\u0647\u0645 \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0639\u0644\u0649 \u0623\u0646\u0647\u0627 \u062F\u0627\u0644\u0629 \u0631\u064A\u0627\u0636\u064A\u0629)\u0645\u0646 \u0641\u0636\u0627\u0621 \u0627\u0644\u0632\u0645\u0646 time domain (\u0623\u064A \u0623\u0646 \u0627\u0644\u0645\u062A\u063A\u064A\u0631 \u0647\u0648 \u0627\u0644\u0632\u0645\u0646) \u0625\u0644\u0649 \u0641\u0636\u0627\u0621 \u0627\u0644\u062A\u0631\u062F\u062F\u0627\u062A Frequency domain (\u0627\u0644\u0645\u062A\u063A\u064A\u0631 \u0647\u0648 \u0627\u0644\u062A\u0631\u062F\u062F). \u0625\u0630\u0646 \u0646\u0638\u0631\u064A\u0627 \u064A\u0643\u0648\u0646 \u0644\u062F\u064A\u0646\u0627 \u062F\u0627\u0644\u0629 \u0645\u062A\u0635\u0644\u0629 \u0646\u0642\u0648\u0645 \u0628\u062A\u062D\u0648\u064A\u0644\u0647\u0627 \u0639\u0646 \u0637\u0631\u064A\u0642 \u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A \u0623\u0648 \u062A\u062D\u0648\u064A\u0644 \u0641\u0648\u0631\u064A\u064A \u0627\u0644\u0639\u0643\u0633\u064A \u0644\u0643\u0646 \u0641\u064A \u0627\u0644\u0648\u0627\u0642\u0639 \u0643\u062B\u064A\u0631\u0627 \u0645\u0627 \u062A\u0639\u062A\u0631\u0636\u0646\u0627 \u0645\u0634\u0627\u0643\u0644 \u0644\u0627 \u064A\u0643\u0648\u0646 \u0644\u062F\u064A\u0646\u0627 \u0641\u064A\u0647\u0627 \u062F\u0627\u0644\u0629 \u0645\u062A\u0635\u0644\u0629 \u0628\u0644 \u0645\u062C\u0645\u0648\u0639\u0629 \u0642\u064A\u0627\u0633\u0627\u062A \u0623\u064A \u0623\u0646\u0647 \u0639\u0648\u0636 \u0623\u0646 \u062A\u0643\u0648\u0646 \u0644\u062F\u064A\u0646\u0627 \u062F\u0627\u0644\u0629 \u0645\u062A\u0635\u0644\u0629 \u062A\u0643\u0648\u0646 \u0644\u062F\u064A\u0646\u0627 \u0645\u062C\u0645\u0648\u0639\u0629 \u0646\u0642\u0627\u0637 \u0647\u064A \u0639\u0628\u0627\u0631\u0629 \u0639\u0644\u0649 \u0642\u064A\u0645\u0629 \u0627\u0644\u062F\u0627\u0644\u0629 \u0641\u064A \u0623\u0632\u0645\u0646\u0629 \u0645\u0639\u064A\u0646\u0629."@ar , "In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discre"@en , "\u79BB\u6563\u5085\u91CC\u53F6\u53D8\u6362\uFF08Discrete Fourier Transform\uFF0C\u7F29\u5199\u4E3ADFT\uFF09\uFF0C\u662F\u5085\u91CC\u53F6\u53D8\u6362\u5728\u65F6\u57DF\u548C\u9891\u57DF\u4E0A\u90FD\u5448\u79BB\u6563\u7684\u5F62\u5F0F\uFF0C\u5C06\u4FE1\u53F7\u7684\u65F6\u57DF\u91C7\u6837\u53D8\u6362\u4E3A\u5176DTFT\u7684\u9891\u57DF\u91C7\u6837\u3002 \u5728\u5F62\u5F0F\u4E0A\uFF0C\u53D8\u6362\u4E24\u7AEF\uFF08\u65F6\u57DF\u548C\u9891\u57DF\u4E0A\uFF09\u7684\u5E8F\u5217\u662F\u6709\u9650\u957F\u7684\uFF0C\u800C\u5B9E\u9645\u4E0A\u8FD9\u4E24\u7EC4\u5E8F\u5217\u90FD\u5E94\u5F53\u88AB\u8BA4\u4E3A\u662F\u79BB\u6563\u5468\u671F\u4FE1\u53F7\u7684\u4E3B\u503C\u5E8F\u5217\u3002\u5373\u4F7F\u5BF9\u6709\u9650\u957F\u7684\u79BB\u6563\u4FE1\u53F7\u4F5CDFT\uFF0C\u4E5F\u5E94\u5F53\u5C06\u5176\u770B\u4F5C\u5176\u5468\u671F\u5EF6\u62D3\u7684\u53D8\u6362\u3002\u5728\u5B9E\u9645\u5E94\u7528\u4E2D\u901A\u5E38\u91C7\u7528\u5FEB\u901F\u5085\u91CC\u53F6\u53D8\u6362\u8BA1\u7B97DFT\u3002"@zh , "Transformasi Fourier Diskrit (TFD) adalah salah satu bentuk transformasi Fourier di mana sebagai ganti integral, digunakan penjumlahan. Dalam matematika sering pula disebut sebagai transformasi Fourier berhingga (finite Fourier transform), yang merupakan suatu transformasi Fourier yang banyak diterapkan dalam pemrosesan sinyal digital dan bidang-bidang terkait untuk menganalisis frekuensi-frekuensi yang terkandung dalam suatu contoh sinyal atau isyarat, untuk menyelesaikan persamaan diferensial parsial, dan untuk melakukan sejumlah operasi, misalnya saja operasi-operasi . TFD ini dapat dihitung secara efesien dalam pemanfaataannya menggunakan algoritme transformasi Fourier cepat (TFC)."@in , "Die Diskrete Fourier-Transformation (DFT) ist eine Transformation aus dem Bereich der Fourier-Analysis.Sie bildet ein zeitdiskretes endliches Signal, das periodisch fortgesetzt wird, auf ein diskretes, periodisches Frequenzspektrum ab, das auch als Bildbereich bezeichnet wird. Die DFT besitzt in der digitalen Signalverarbeitung zur Signalanalyse gro\u00DFe Bedeutung. Hier werden optimierte Varianten in Form der schnellen Fourier-Transformation (englisch fast Fourier transform, FFT) und ihrer Inversen angewandt. Die DFT wird in der Signalverarbeitung f\u00FCr viele Aufgaben verwendet, so z. B."@de , "La transformation de Fourier discr\u00E8te (TFD), outil math\u00E9matique, sert \u00E0 traiter un signal num\u00E9rique. Elle constitue un \u00E9quivalent discret de la transformation de Fourier (continue) utilis\u00E9e pour traiter un signal analogique. La transformation de Fourier rapide est un algorithme particulier de calcul de la transformation de Fourier discr\u00E8te. Sa d\u00E9finition pour un signal de \u00E9chantillons est la suivante : . La transformation inverse est donn\u00E9e par : . On obtient ainsi une repr\u00E9sentation spectrale discr\u00E8te du signal \u00E9chantillonn\u00E9 ."@fr , "\u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\uFF08\u308A\u3055\u3093\u30D5\u30FC\u30EA\u30A8\u3078\u3093\u304B\u3093\u3001\u82F1\u8A9E: discrete Fourier transform\u3001DFT\uFF09\u3068\u306F\u6B21\u5F0F\u3067\u5B9A\u7FA9\u3055\u308C\u308B\u5909\u63DB\u3067\u3001\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u306B\u985E\u4F3C\u3057\u305F\u3082\u306E\u3067\u3042\u308A\u3001\u4FE1\u53F7\u51E6\u7406\u306A\u3069\u3067\u96E2\u6563\u5316\u3055\u308C\u305F\u30C7\u30B8\u30BF\u30EB\u4FE1\u53F7\u306E\u5468\u6CE2\u6570\u89E3\u6790\u306A\u3069\u306B\u3088\u304F\u4F7F\u308F\u308C\u308B\u3002\u307E\u305F\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3084\u7573\u307F\u8FBC\u307F\u7A4D\u5206\u306E\u6570\u5024\u8A08\u7B97\u3092\u52B9\u7387\u7684\u306B\u884C\u3046\u305F\u3081\u306B\u3082\u4F7F\u308F\u308C\u308B\u3002\u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u306F\uFF08\u8A08\u7B97\u6A5F\u4E0A\u3067\uFF09\u9AD8\u901F\u30D5\u30FC\u30EA\u30A8\u5909\u63DB(FFT)\u3092\u4F7F\u3063\u3066\u9AD8\u901F\u306B\u8A08\u7B97\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u3068\u306F\u3001\u8907\u7D20\u95A2\u6570 \u3092\u8907\u7D20\u95A2\u6570\u306B\u5199\u3059\u5199\u50CF\u3067\u3042\u3063\u3066\u3001\u6B21\u306E\u5F0F\u3067\u5B9A\u7FA9\u3055\u308C\u308B\u3082\u306E\u3092\u8A00\u3046\u3002 \u3053\u3053\u3067\u3001N\u306F\u4EFB\u610F\u306E\u81EA\u7136\u6570\u3001 \u306F\u30CD\u30A4\u30D4\u30A2\u6570\u3001 \u306F\u865A\u6570\u5358\u4F4D\u3067\u3001\u306F\u5186\u5468\u7387\u3067\u3042\u308B\u3002\u3053\u306E\u3068\u304D\u3001{}\u3092\u6A19\u672C\u70B9\u3068\u3044\u3046\u3002\u307E\u305F\u3001\u3053\u306E\u5909\u63DB\u3092 \u3068\u3044\u3046\u8A18\u53F7\u3067\u8868\u3057\u3001 \u306E\u3088\u3046\u306B\u7565\u8A18\u3059\u308B\u3053\u3068\u304C\u591A\u3044\u3002 \u3053\u306E\u9006\u5909\u63DB\u306B\u3042\u305F\u308B\u9006\u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\uFF08\u82F1\u8A9E: inverse discrete Fourier transform\u3001IDFT\uFF09\u306F"@ja , "Diskret fouriertransform, p\u00E5 engelska discrete Fourier transform (DFT), \u00E4r inom matematiken en specifik typ av diskret transform som anv\u00E4nds i fourieranalys. Den transformerar en funktion till en annan som kallas frekvensdom\u00E4ns-representation, eller helt enkelt DFT, fr\u00E5n originalfunktionen, som ofta \u00E4r en funktion i tidsdom\u00E4nen."@sv , "En matem\u00E0tica aplicada, i m\u00E9s particularment en teoria del senyal, la transformada discreta de Fourier o transformada de Fourier discreta, a vegades denotada per l'acr\u00F2nim DFT de l'angl\u00E8s discrete Fourier transform, \u00E9s un tipus de transformada discreta usat en el processament del senyal digital, an\u00E0leg a la transformada de Fourier per al processament del senyal anal\u00F2gic."@ca , "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0435 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0424\u0443\u0440'\u0454 (\u0414\u041F\u0424, \u0430\u043D\u0433\u043B. Discrete Fourier Transform) \u2014 \u0446\u0435 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0430 \u043F\u0440\u043E\u0446\u0435\u0434\u0443\u0440\u0430, \u0449\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0434\u043B\u044F \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0433\u0430\u0440\u043C\u043E\u043D\u0456\u0447\u043D\u043E\u0433\u043E, \u0430\u0431\u043E \u0447\u0430\u0441\u0442\u043E\u0442\u043D\u043E\u0433\u043E, \u0441\u043A\u043B\u0430\u0434\u0443 \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0438\u0445 \u0441\u0438\u0433\u043D\u0430\u043B\u0456\u0432. \u0414\u041F\u0424 \u0454 \u043E\u0434\u043D\u0456\u0454\u044E \u0437 \u043D\u0430\u0439\u0431\u0456\u043B\u044C\u0448 \u0440\u043E\u0437\u043F\u043E\u0432\u0441\u044E\u0434\u0436\u0435\u043D\u0438\u0445 \u0456 \u043F\u043E\u0442\u0443\u0436\u043D\u0438\u0445 \u043F\u0440\u043E\u0446\u0435\u0434\u0443\u0440 \u0446\u0438\u0444\u0440\u043E\u0432\u043E\u0457 \u043E\u0431\u0440\u043E\u0431\u043A\u0438 \u0441\u0438\u0433\u043D\u0430\u043B\u0456\u0432. \u0414\u041F\u0424 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u0430\u043D\u0430\u043B\u0456\u0437\u0443\u0432\u0430\u0442\u0438, \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u044E\u0432\u0430\u0442\u0438 \u0456 \u0441\u0438\u043D\u0442\u0435\u0437\u0443\u0432\u0430\u0442\u0438 \u0441\u0438\u0433\u043D\u0430\u043B\u0438 \u0442\u0430\u043A\u0438\u043C\u0438 \u0441\u043F\u043E\u0441\u043E\u0431\u0430\u043C\u0438, \u044F\u043A\u0456 \u043D\u0435\u043C\u043E\u0436\u043B\u0438\u0432\u0456 \u043F\u0440\u0438 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0456\u0439 (\u0430\u043D\u0430\u043B\u043E\u0433\u043E\u0432\u0456\u0439) \u043E\u0431\u0440\u043E\u0431\u0446\u0456."@uk , "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435 (\u0432 \u0430\u043D\u0433\u043B\u043E\u044F\u0437\u044B\u0447\u043D\u043E\u0439 \u043B\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0435 DFT, Discrete Fourier Transform) \u2014 \u044D\u0442\u043E \u043E\u0434\u043D\u043E \u0438\u0437 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0439 \u0424\u0443\u0440\u044C\u0435, \u0448\u0438\u0440\u043E\u043A\u043E \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u0435\u043C\u044B\u0445 \u0432 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0430\u0445 \u0446\u0438\u0444\u0440\u043E\u0432\u043E\u0439 \u043E\u0431\u0440\u0430\u0431\u043E\u0442\u043A\u0438 \u0441\u0438\u0433\u043D\u0430\u043B\u043E\u0432 (\u0435\u0433\u043E \u043C\u043E\u0434\u0438\u0444\u0438\u043A\u0430\u0446\u0438\u0438 \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u044E\u0442\u0441\u044F \u0432 \u0441\u0436\u0430\u0442\u0438\u0438 \u0437\u0432\u0443\u043A\u0430 \u0432 MP3, \u0441\u0436\u0430\u0442\u0438\u0438 \u0438\u0437\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u0438\u0439 \u0432 JPEG \u0438 \u0434\u0440.), \u0430 \u0442\u0430\u043A\u0436\u0435 \u0432 \u0434\u0440\u0443\u0433\u0438\u0445 \u043E\u0431\u043B\u0430\u0441\u0442\u044F\u0445, \u0441\u0432\u044F\u0437\u0430\u043D\u043D\u044B\u0445 \u0441 \u0430\u043D\u0430\u043B\u0438\u0437\u043E\u043C \u0447\u0430\u0441\u0442\u043E\u0442 \u0432 \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u043C (\u043A \u043F\u0440\u0438\u043C\u0435\u0440\u0443, \u043E\u0446\u0438\u0444\u0440\u043E\u0432\u0430\u043D\u043D\u043E\u043C \u0430\u043D\u0430\u043B\u043E\u0433\u043E\u0432\u043E\u043C) \u0441\u0438\u0433\u043D\u0430\u043B\u0435. \u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435 \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u0432 \u043A\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0432\u0445\u043E\u0434\u0430 \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0443\u044E \u0444\u0443\u043D\u043A\u0446\u0438\u044E. \u0422\u0430\u043A\u0438\u0435 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u0447\u0430\u0441\u0442\u043E \u0441\u043E\u0437\u0434\u0430\u044E\u0442\u0441\u044F \u043F\u0443\u0442\u0451\u043C \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u0438\u0437\u0430\u0446\u0438\u0438 (\u0432\u044B\u0431\u043E\u0440\u043A\u0438 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u0439 \u0438\u0437 \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u044B\u0445 \u0444\u0443\u043D\u043A\u0446\u0438\u0439). \u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u044B\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u044F \u0424\u0443\u0440\u044C\u0435 \u043F\u043E\u043C\u043E\u0433\u0430\u044E\u0442 \u0440\u0435\u0448\u0430\u0442\u044C \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u0435 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445 \u0438 \u0432\u044B\u043F\u043E\u043B\u043D\u044F\u0442\u044C \u0442\u0430\u043A\u0438\u0435 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u0438, \u043A\u0430\u043A \u0441\u0432\u0451\u0440\u0442\u043A\u0438. \u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u044B\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u044F \u0424\u0443\u0440\u044C\u0435 \u0442\u0430\u043A\u0436\u0435 \u0430\u043A\u0442\u0438\u0432\u043D\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u044E\u0442\u0441\u044F \u0432 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043A\u0435, \u043F\u0440\u0438 \u0430\u043D\u0430\u043B\u0438\u0437\u0435 \u0432\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0445 \u0440\u044F\u0434\u043E\u0432. \u0421\u0443\u0449"@ru , "Dyskretna transformata Fouriera (ang. Discrete Fourier Transform, DFT) \u2013 transformata Fouriera wyznaczona dla sygna\u0142u pr\u00F3bkowanego, a wi\u0119c dyskretnego."@pl , "In de wiskunde is de discrete fouriertransformatie of DFT een fouriertransformatie die veel wordt toegepast in de digitale signaalverwerking en verwante vakgebieden voor het analyseren van de frequenties die aanwezig zijn in een bemonsterd signaal, en voor het uitvoeren van bewerkingen zoals discrete convoluties. De DFT kan effici\u00EBnt worden berekend door gebruik te maken van het FFT-algoritme. De rij van complexe getallen wordt door de DFT getransformeerd in de rij van complexe getallen volgens de formule: en . De inverse discrete fouriertransformatie (IDFT) wordt gegeven door"@nl , "Para sequ\u00EAncias de dura\u00E7\u00E3o finita, existe uma representa\u00E7\u00E3o de Fourier em tempo discreto alternativa, chamada de transformada de Fourier discreta (TFD). A TFD \u00E9 uma sequ\u00EAncia, em vez de uma fun\u00E7\u00E3o de vari\u00E1vel cont\u00EDnua, e corresponde a amostras em frequ\u00EAncia, igualmente espa\u00E7adas, da TFTD do sinal."@pt , "En matem\u00E1ticas, la transformada discreta de Fourier o DFT (del ingl\u00E9s, discrete Fourier transform) es un tipo de utilizada en el an\u00E1lisis de Fourier. Transforma una funci\u00F3n matem\u00E1tica en otra, obteniendo una representaci\u00F3n en el dominio de la frecuencia, siendo la funci\u00F3n original una funci\u00F3n en el dominio del tiempo. Pero la DFT requiere que la funci\u00F3n de entrada sea una secuencia discreta y de duraci\u00F3n finita. Dichas secuencias se suelen generar a partir del muestreo de una funci\u00F3n continua, como puede ser la voz humana. Al contrario que la (DTFT), esta transformaci\u00F3n \u00FAnicamente eval\u00FAa suficientes componentes frecuenciales para reconstruir el segmento finito que se analiza. Utilizar la DFT implica que el segmento que se analiza es un \u00FAnico per\u00EDodo de una se\u00F1al peri\u00F3dica que se extiende"@es . @prefix foaf: . dbr:Discrete_Fourier_transform foaf:depiction , , . @prefix dcterms: . @prefix dbc: . dbr:Discrete_Fourier_transform dcterms:subject dbc:Unitary_operators , dbc:Numerical_analysis , dbc:Discrete_transforms , dbc:Fourier_analysis , dbc:Digital_signal_processing . @prefix dbo: . dbr:Discrete_Fourier_transform dbo:wikiPageID 8811 ; dbo:wikiPageRevisionID 1122611963 ; dbo:wikiPageWikiLink dbr:Multiplication_algorithms , dbr:Discrete_cosine_transform , dbr:Fast_Fourier_transform , dbr:Multidimensional_transform , dbr:Companion_matrix , dbc:Unitary_operators , dbr:Sinc , dbr:Primitive_root_of_unity , dbr:Defective_matrix , dbr:Finite_group , dbr:Even_and_odd_functions , dbr:Binomial_theorem , dbr:Kronecker_delta , dbr:Cross_correlation , dbr:Variance , dbr:Wavelet_transform , dbr:Discrete-time_Fourier_transform , dbr:Cross-correlation , dbr:Raster_image , dbr:Kronecker_comb , dbr:Bandlimited , , dbr:Initialism , , dbr:Discrete_Fourier_series , dbc:Numerical_analysis , dbr:Discrete_Fourier_transform , , dbr:Circulant_matrix , dbr:Discrete_Hartley_transform , dbr:Nyquist_frequency , dbr:Periodic_summation , dbr:Orthonormal , dbr:List_of_Fourier-related_transforms , dbr:Sequence , dbr:Vandermonde_matrix , dbr:Commutative_operation , dbr:JPEG2000 , dbr:Periodogram , , , dbr:Overlap-save_method , dbr:Dirichlet_kernel , dbr:Complex_conjugate , dbr:JPEG , dbr:Least-squares_spectral_analysis , dbr:Wavelets , dbc:Discrete_transforms , dbr:Unitary_operator , dbr:Quantum_Fourier_transform , dbr:Matched_filter , dbr:Characteristic_polynomial , dbr:Gaussian_distribution , dbr:Spectral_leakage , dbr:Orthogonality , , dbr:Hermite_function , dbr:Heisenberg_uncertainty_principle , dbr:Number-theoretic_transform , dbr:Probability_mass_function , dbr:Composite_number , dbr:Spectral_method , dbr:Unitary_matrix , , dbr:Function_composition , , dbr:Jacobi_theta_function , , , dbr:Linearly_independent , , , dbr:Linear_differential_equation , dbr:Algebraic_multiplicity , dbr:Computer , dbr:Determinant , dbr:Discrete_wavelet_transform , dbr:Fractional_Fourier_transform , dbr:Mathematics , , dbr:Orthogonal_basis , dbr:Welch_method , dbr:Z-transform , dbr:Sine_wave , dbr:Fourier_transform_on_finite_groups , dbr:Linear_transformation , dbr:Partial_differential_equations , dbr:Discretization , dbr:Real_number , , dbr:Real_numbers , dbr:Modified_discrete_cosine_transform , dbr:Roots_of_unity , dbr:DFT_matrix , dbr:Entropic_uncertainty , dbr:Projection-slice_theorem , dbr:Frequency , dbr:Class_function , dbr:Window_function , dbr:Spectral_estimation , dbr:Odd_integer , dbr:Root_of_unity , dbr:Eigenvalue , dbr:Eigenvector , dbr:Unitary_transformation , dbr:Discrete_transform , dbr:Signal_spectral_analysis , dbr:Identity_matrix , , dbr:Discrete_sine_transform , dbr:Carl_Friedrich_Gauss , dbr:Spectrogram , dbr:Image_processing , dbc:Fourier_analysis , dbr:Plane_wave , dbr:Coordinate_vector , dbr:Digital_signal_processing , dbr:Geometric_progression , dbr:Periodic_sequence , dbr:Continuous_Fourier_transform , dbr:Bartlett_method , , dbr:Numerical_algorithm , dbr:Generalizations_of_Pauli_matrices , dbr:Direct_current , dbr:Digital_image_processing , , dbr:FFTW , dbr:Complex_number , dbr:Zak_transform , dbr:Integer , dbr:Sound_wave , dbr:Plancherel_theorem , dbr:Geometric_series , dbr:Representation_theory_of_finite_groups , dbr:Circular_convolution , dbr:Kravchuk_polynomials , dbr:Trigonometric_interpolation_polynomial , dbc:Digital_signal_processing , dbr:Frequency_domain , dbr:Mean , dbr:Radio , dbr:Arctan , dbr:Aliasing , , dbr:Digital_circuit , dbr:Pixel , dbr:Atan2 , dbr:Gaussian_function , dbr:Fourier_series , dbr:Fourier_transform , dbr:Cyclic_group , dbr:Nyquist_rate , dbr:Modular_arithmetic , dbr:Representation_theory , dbr:Convolution , dbr:Orthonormal_basis , dbr:Finite_field , dbr:Convolution_theorem , dbr:Sign_convention , dbr:Fourier_analysis , dbr:Temperature , dbr:FFTPACK , dbr:DTFT , , dbr:Matrix_polynomial , dbr:Lossy_compression , ; dbo:wikiPageExternalLink , , , . @prefix ns9: . dbr:Discrete_Fourier_transform dbo:wikiPageExternalLink ns9:the_discrete_fourier_transformation_dft , , , , , , , . @prefix ns10: . dbr:Discrete_Fourier_transform dbo:wikiPageExternalLink ns10:the_discrete_fourier_transformation_dft . @prefix ns11: . dbr:Discrete_Fourier_transform dbo:wikiPageExternalLink ns11:n844 , , ; owl:sameAs , , . @prefix dbpedia-sv: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-sv:Diskret_fouriertransform . @prefix dbpedia-es: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-es:Transformada_de_Fourier_discreta . @prefix ns14: . dbr:Discrete_Fourier_transform owl:sameAs ns14:Transformasi_Fourier_Diskrit , . @prefix wikidata: . dbr:Discrete_Fourier_transform owl:sameAs wikidata:Q2878 , , , . @prefix yago-res: . dbr:Discrete_Fourier_transform owl:sameAs yago-res:Discrete_Fourier_transform . @prefix dbpedia-de: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-de:Diskrete_Fourier-Transformation , . @prefix dbpedia-id: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-id:Transformasi_Fourier_diskrit . @prefix dbpedia-pl: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-pl:Dyskretna_transformata_Fouriera , . @prefix dbpedia-sh: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-sh:Diskretna_furijeova_transformacija . @prefix dbpedia-nl: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-nl:Discrete_fouriertransformatie . @prefix dbpedia-it: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-it:Trasformata_discreta_di_Fourier , , , , , , , . @prefix dbpedia-ca: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-ca:Transformada_discreta_de_Fourier , . @prefix dbpedia-pt: . dbr:Discrete_Fourier_transform owl:sameAs dbpedia-pt:Transformada_discreta_de_Fourier . @prefix dbp: . @prefix dbt: . dbr:Discrete_Fourier_transform dbp:wikiPageUsesTemplate dbt:Slink , dbt:Efn-ua , dbt:Rp , dbt:Notelist-ua , dbt:Main , dbt:NumBlk , dbt:Short_description , dbt:Unordered_list , dbt:EquationRef , dbt:Anchor , dbt:Fourier_transforms , dbt:Webarchive , dbt:Equation_box_1 , dbt:Reflist , dbt:Mvar , dbt:Distinguish , dbt:Details , dbt:Math , dbt:DSP , dbt:EquationNote , dbt:Cite_book , dbt:Cite_journal ; dbo:thumbnail . @prefix dbpedia-cs: . dbr:Discrete_Fourier_transform dbo:wikiPageInterLanguageLink dbpedia-cs:Fourierova_transformace , dbpedia-pt:Transformada_de_Fourier , . @prefix xsd: . dbr:Discrete_Fourier_transform dbp:date "2016-03-04"^^xsd:date ; dbp:url ns10:the_discrete_fourier_transformation_dft ; dbo:abstract "\u03A3\u03C4\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC, \u03BF \u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03CC\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourier (DFT) \u03BC\u03B5\u03C4\u03B1\u03C4\u03C1\u03AD\u03C0\u03B5\u03B9 \u03BC\u03B9\u03B1 \u03C0\u03B5\u03C0\u03B5\u03C1\u03B1\u03C3\u03BC\u03AD\u03BD\u03B7 \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03AF\u03B1 \u03B1\u03C0\u03CC \u03AF\u03C3\u03B1 \u03B4\u03B9\u03B1\u03C3\u03C4\u03AE\u03BC\u03B1\u03C4\u03B1 \u03B4\u03B5\u03B9\u03B3\u03BC\u03AC\u03C4\u03C9\u03BD \u03B1\u03C0\u03CC \u03BC\u03B9\u03B1 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7 \u03C3\u03B5 \u03BC\u03AF\u03B1 \u03BB\u03AF\u03C3\u03C4\u03B1 \u03BC\u03B5 \u03C3\u03C5\u03BD\u03C4\u03B5\u03BB\u03B5\u03C3\u03C4\u03AD\u03C2 \u03B1\u03C0\u03CC \u03AD\u03BD\u03B1 \u03C0\u03B5\u03C0\u03B5\u03C1\u03B1\u03C3\u03BC\u03AD\u03BD\u03BF \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03BC\u03CC \u03B7\u03BC\u03B9\u03C4\u03BF\u03BD\u03BF\u03B5\u03B9\u03B4\u03CE\u03BD \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CE\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD, \u03BA\u03B1\u03B8\u03BF\u03C1\u03B9\u03C3\u03BC\u03AD\u03BD\u03C9\u03BD \u03B1\u03C0\u03CC \u03C4\u03B9\u03C2 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B5\u03C2 \u03C4\u03BF\u03C5\u03C2, \u03C0\u03BF\u03C5 \u03AD\u03C7\u03B5\u03B9 \u03C4\u03B9\u03C2 \u03AF\u03B4\u03B9\u03B5\u03C2 \u03C4\u03B9\u03BC\u03AD\u03C2 \u03B4\u03B5\u03AF\u03B3\u03BC\u03B1\u03C4\u03BF\u03C2. \u0391\u03C5\u03C4\u03CC \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03B5\u03B9\u03C0\u03C9\u03B8\u03B5\u03AF \u03B3\u03B9\u03B1 \u03C4\u03B7 \u03BC\u03B5\u03C4\u03B1\u03C4\u03C1\u03BF\u03C0\u03AE \u03C4\u03BF\u03C5 \u03B4\u03B5\u03AF\u03B3\u03BC\u03B1\u03C4\u03BF\u03C2 \u03C4\u03B7\u03C2 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7\u03C2 \u03B1\u03C0\u03CC \u03C4\u03BF \u03B1\u03C1\u03C7\u03B9\u03BA\u03CC \u03C4\u03BF\u03C5 \u03C0\u03B5\u03B4\u03AF\u03BF \u03BF\u03C1\u03B9\u03C3\u03BC\u03BF\u03CD (\u03C3\u03C5\u03C7\u03BD\u03AC \u03C4\u03BF \u03C7\u03C1\u03CC\u03BD\u03BF \u03AE \u03C4\u03B7 \u03B8\u03AD\u03C3\u03B7 \u03BA\u03B1\u03C4\u03AC \u03BC\u03AE\u03BA\u03BF\u03C2 \u03C4\u03B7\u03C2 \u03B3\u03C1\u03B1\u03BC\u03BC\u03AE\u03C2) \u03C3\u03C4\u03BF \u03C0\u03B5\u03B4\u03AF\u03BF \u03C4\u03B7\u03C2 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2. \u03A4\u03B1 \u03B4\u03B5\u03AF\u03B3\u03BC\u03B1\u03C4\u03B1 \u03B5\u03B9\u03C3\u03B1\u03B3\u03C9\u03B3\u03AE\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03BF\u03AF \u03B1\u03C1\u03B9\u03B8\u03BC\u03BF\u03AF (\u03C3\u03C4\u03B7\u03BD \u03C0\u03C1\u03AC\u03BE\u03B7, \u03C3\u03C5\u03BD\u03AE\u03B8\u03C9\u03C2 \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03BF\u03AF \u03B1\u03C1\u03B9\u03B8\u03BC\u03BF\u03AF), \u03BA\u03B1\u03B9 \u03BF\u03B9 \u03C3\u03C5\u03BD\u03C4\u03B5\u03BB\u03B5\u03C3\u03C4\u03AD\u03C2 \u03C3\u03C4\u03BF \u03B1\u03C0\u03BF\u03C4\u03AD\u03BB\u03B5\u03C3\u03BC\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BA\u03B1\u03B9 \u03B1\u03C5\u03C4\u03BF\u03AF \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03BF\u03AF . \u039F\u03B9 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B5\u03C2 \u03C4\u03C9\u03BD \u03B7\u03BC\u03B9\u03C4\u03BF\u03BD\u03BF\u03B5\u03B9\u03B4\u03CE\u03BD \u03C0\u03BF\u03C5 \u03C0\u03C1\u03BF\u03BA\u03CD\u03C0\u03C4\u03BF\u03C5\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B1\u03BA\u03AD\u03C1\u03B1\u03B9\u03B1 \u03C0\u03BF\u03BB\u03BB\u03B1\u03C0\u03BB\u03AC\u03C3\u03B9\u03B1 \u03C4\u03B7\u03C2 \u03B8\u03B5\u03BC\u03B5\u03BB\u03B9\u03CE\u03B4\u03BF\u03C5\u03C2 \u03C3\u03C5\u03C7\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2, \u03C4\u03BF\u03C5 \u03BF\u03C0\u03BF\u03AF\u03BF\u03C5 \u03B7 \u03B1\u03BD\u03C4\u03AF\u03C3\u03C4\u03BF\u03B9\u03C7\u03B7 \u03C0\u03B5\u03C1\u03AF\u03BF\u03B4\u03BF \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C4\u03BF \u03BC\u03AE\u03BA\u03BF\u03C2 \u03C4\u03BF\u03C5 \u03B4\u03B9\u03B1\u03C3\u03C4\u03AE\u03BC\u03B1\u03C4\u03BF\u03C2 \u03B4\u03B5\u03B9\u03B3\u03BC\u03B1\u03C4\u03BF\u03BB\u03B7\u03C8\u03AF\u03B1\u03C2. \u039F \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03BC\u03CC\u03C2 \u03C4\u03C9\u03BD \u03B7\u03BC\u03B9\u03C4\u03BF\u03BD\u03BF\u03B5\u03B9\u03B4\u03CE\u03BD \u03C0\u03BF\u03C5 \u03BB\u03B1\u03BC\u03B2\u03AC\u03BD\u03BF\u03BD\u03C4\u03B1\u03B9 \u03BC\u03AD\u03C3\u03C9 \u03C4\u03BF\u03C5 DFT \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C0\u03BF\u03BC\u03AD\u03BD\u03C9\u03C2 \u03C0\u03B5\u03C1\u03B9\u03BF\u03B4\u03B9\u03BA\u03AE \u03BC\u03B5 \u03C4\u03B7\u03BD \u03AF\u03B4\u03B9\u03B1 \u03C0\u03B5\u03C1\u03AF\u03BF\u03B4\u03BF. \u039F DFT(\u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03CC\u03C2 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC\u03C2 Fourie) \u03B4\u03B9\u03B1\u03C6\u03AD\u03C1\u03B5\u03B9 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03BF\u03CD \u03C7\u03C1\u03CC\u03BD\u03BF\u03C5 \u03BC\u03B5\u03C4\u03B1\u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03B9\u03C3\u03BC\u03CC Fourier (DTFT) \u03C3\u03C4\u03B7\u03BD \u03B5\u03AF\u03C3\u03BF\u03B4\u03BF \u03C4\u03BF\u03C5\u03C2 \u03BA\u03B1\u03B9 \u03C3\u03C4\u03BF \u03B1\u03C0\u03BF\u03C4\u03AD\u03BB\u03B5\u03C3\u03BC\u03B1 \u03BF\u03B9 \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03AF\u03B5\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BA\u03B1\u03B9 \u03BF\u03B9 \u03B4\u03CD\u03BF \u03C0\u03B5\u03C0\u03B5\u03C1\u03B1\u03C3\u03BC\u03AD\u03BD\u03B5\u03C2, \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C9\u03C2 \u03B5\u03BA \u03C4\u03BF\u03CD\u03C4\u03BF\u03C5 \u03B7 \u03BB\u03B5\u03B3\u03CC\u03BC\u03B5\u03BD\u03B7 \u03B1\u03BD\u03AC\u03BB\u03C5\u03C3\u03B7 Fourier \u03C4\u03C9\u03BD \u03C0\u03B5\u03C0\u03B5\u03C1\u03B1\u03C3\u03BC\u03AD\u03BD\u03C9\u03BD (\u03AE \u03C0\u03B5\u03C1\u03B9\u03BF\u03B4\u03B9\u03BA\u03CE\u03BD) \u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03BF\u03CD \u03C7\u03C1\u03CC\u03BD\u03BF\u03C5 \u03C3\u03C5\u03BD\u03B1\u03C1\u03C4\u03AE\u03C3\u03B5\u03C9\u03BD. \u039F DFT \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BF \u03C0\u03B9\u03BF 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\u0627\u0644\u0645\u062A\u0642\u0637\u0639 \u0648\u0646\u062D\u0635\u0644 \u0639\u0644\u0649 \u0635\u064A\u063A\u0629 \u064A\u0645\u0643\u0646\u0646\u0627 \u0641\u064A\u0647\u0627 \u0631\u0624\u064A\u0629 \u0627\u0644\u0630\u0628\u0630\u0628\u0627\u062A \u0627\u0644\u0645\u062A\u0648\u0627\u062C\u062F\u0629 \u0641\u064A \u0627\u0644\u0642\u064A\u0627\u0633 \u0627\u0644\u0630\u064A \u0642\u0645\u0646\u0627 \u0628\u0647 \u0648\u062A\u0635\u0645\u064A\u0645 \u0622\u0644\u0627\u062A (\u0647\u064A \u0646\u0638\u0631\u064A\u0627 \u0645\u0631\u0634\u062D\u0627\u062A) \u0644\u0644\u062D\u062F \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0630\u0628\u0630\u0628\u0627\u062A \u0623\u0648 \u0627\u0644\u0627\u0647\u062A\u0632\u0627\u0632\u0627\u062A."@ar , "\uC774\uC0B0 \uD478\uB9AC\uC5D0 \uBCC0\uD658(discrete Fourier transform, DFT)\uC740 \uC774\uC0B0\uC801\uC778 \uC785\uB825 \uC2E0\uD638\uC5D0 \uB300\uD55C \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC73C\uB85C, \uB514\uC9C0\uD138 \uC2E0\uD638 \uBD84\uC11D\uACFC \uAC19\uC740 \uBD84\uC57C\uC5D0 \uC0AC\uC6A9\uB41C\uB2E4. \uC774\uC0B0 \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC740 \uACE0\uC18D \uD478\uB9AC\uC5D0 \uBCC0\uD658\uC744 \uC774\uC6A9\uD574 \uBE60\uB974\uAC8C \uACC4\uC0B0\uD560 \uC218 \uC788\uB2E4."@ko , "En matem\u00E0tica aplicada, i m\u00E9s particularment en teoria del senyal, la transformada discreta de Fourier o transformada de Fourier discreta, a vegades denotada per l'acr\u00F2nim DFT de l'angl\u00E8s discrete Fourier transform, \u00E9s un tipus de transformada discreta usat en el processament del senyal digital, an\u00E0leg a la transformada de Fourier per al processament del senyal anal\u00F2gic."@ca , "La transformation de Fourier discr\u00E8te (TFD), outil math\u00E9matique, sert \u00E0 traiter un signal num\u00E9rique. Elle constitue un \u00E9quivalent discret de la transformation de Fourier (continue) utilis\u00E9e pour traiter un signal analogique. La transformation de Fourier rapide est un algorithme particulier de calcul de la transformation de Fourier discr\u00E8te. Sa d\u00E9finition pour un signal de \u00E9chantillons est la suivante : . La transformation inverse est donn\u00E9e par : . On obtient ainsi une repr\u00E9sentation spectrale discr\u00E8te du signal \u00E9chantillonn\u00E9 . La TFD ne calcule pas le spectre continu d'un signal continu. Elle permet seulement d'\u00E9valuer une repr\u00E9sentation spectrale discr\u00E8te (spectre \u00E9chantillonn\u00E9) d'un signal discret (signal \u00E9chantillonn\u00E9) sur une fen\u00EAtre de temps finie (\u00E9chantillonnage born\u00E9 dans le temps). L'exemple ci-dessous peut laisser croire que la TFD permet de calculer le spectre d'un signal continu, mais cela n'arrive que lorsque la fen\u00EAtre d'\u00E9chantillonnage correspond \u00E0 un multiple strictement sup\u00E9rieur \u00E0 deux fois la p\u00E9riode du signal \u00E9chantillonn\u00E9 (dans ce cas on a forc\u00E9ment \u00E9vit\u00E9 le repliement de spectre, c'est le th\u00E9or\u00E8me d'\u00E9chantillonnage de Nyquist-Shannon) : Ces d\u00E9finitions ne sont pas uniques : on peut tout \u00E0 fait normer la TFD par , et ne pas normer la TFD inverse, ou encore normer les deux par , le but \u00E9tant dans tous les cas de retrouver le signal originel par la TFD inverse de sa TFD. La TFD correspond \u00E0 l'\u00E9valuation sur le cercle unit\u00E9 de la transform\u00E9e en Z pour des valeurs discr\u00E8tes de la fr\u00E9quence."@fr , "Para sequ\u00EAncias de dura\u00E7\u00E3o finita, existe uma representa\u00E7\u00E3o de Fourier em tempo discreto alternativa, chamada de transformada de Fourier discreta (TFD). A TFD \u00E9 uma sequ\u00EAncia, em vez de uma fun\u00E7\u00E3o de vari\u00E1vel cont\u00EDnua, e corresponde a amostras em frequ\u00EAncia, igualmente espa\u00E7adas, da TFTD do sinal."@pt , "Transformasi Fourier Diskrit (TFD) adalah salah satu bentuk transformasi Fourier di mana sebagai ganti integral, digunakan penjumlahan. Dalam matematika sering pula disebut sebagai transformasi Fourier berhingga (finite Fourier transform), yang merupakan suatu transformasi Fourier yang banyak diterapkan dalam pemrosesan sinyal digital dan bidang-bidang terkait untuk menganalisis frekuensi-frekuensi yang terkandung dalam suatu contoh sinyal atau isyarat, untuk menyelesaikan persamaan diferensial parsial, dan untuk melakukan sejumlah operasi, misalnya saja operasi-operasi . TFD ini dapat dihitung secara efesien dalam pemanfaataannya menggunakan algoritme transformasi Fourier cepat (TFC). Dikarenakan TFC umumnya digunakan untuk menghitung TFD, dua istilah ini sering dipetukarkan dalam penggunaannya, walaupun terdapat perbedaan yang jelas antara keduanya: \"TFD\" merujuk pada suatu transformasi matematik bebas atau tidak bergantung bagaimana transformasi tersebut dihitung, sedangkan \"TFC\" merujuk pada satu atau beberapa algoritme efesien untuk menghitung TFD. Lebih jauh, pembedaan ini menjadi semakin membingungkan, misalnya dengan sinonim \"transformasi fourier berhingga\" (dalam bahasa Inggris finite Fourier transform dibandingkan dengan fast Fourier transform yang sama-sama memiliki singkatan FFT), yang mendahului penggunaan istilah \"transformasi fourier cepat\" (Cooley et al., 1969). Untungnya dalam bahasa Indonesia, hal ini tidak terlalu membingungkan."@in , "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0435 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0424\u0443\u0440'\u0454 (\u0414\u041F\u0424, \u0430\u043D\u0433\u043B. Discrete Fourier Transform) \u2014 \u0446\u0435 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0430 \u043F\u0440\u043E\u0446\u0435\u0434\u0443\u0440\u0430, \u0449\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0434\u043B\u044F \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0433\u0430\u0440\u043C\u043E\u043D\u0456\u0447\u043D\u043E\u0433\u043E, \u0430\u0431\u043E \u0447\u0430\u0441\u0442\u043E\u0442\u043D\u043E\u0433\u043E, \u0441\u043A\u043B\u0430\u0434\u0443 \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0438\u0445 \u0441\u0438\u0433\u043D\u0430\u043B\u0456\u0432. \u0414\u041F\u0424 \u0454 \u043E\u0434\u043D\u0456\u0454\u044E \u0437 \u043D\u0430\u0439\u0431\u0456\u043B\u044C\u0448 \u0440\u043E\u0437\u043F\u043E\u0432\u0441\u044E\u0434\u0436\u0435\u043D\u0438\u0445 \u0456 \u043F\u043E\u0442\u0443\u0436\u043D\u0438\u0445 \u043F\u0440\u043E\u0446\u0435\u0434\u0443\u0440 \u0446\u0438\u0444\u0440\u043E\u0432\u043E\u0457 \u043E\u0431\u0440\u043E\u0431\u043A\u0438 \u0441\u0438\u0433\u043D\u0430\u043B\u0456\u0432. \u0414\u041F\u0424 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u0430\u043D\u0430\u043B\u0456\u0437\u0443\u0432\u0430\u0442\u0438, \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u044E\u0432\u0430\u0442\u0438 \u0456 \u0441\u0438\u043D\u0442\u0435\u0437\u0443\u0432\u0430\u0442\u0438 \u0441\u0438\u0433\u043D\u0430\u043B\u0438 \u0442\u0430\u043A\u0438\u043C\u0438 \u0441\u043F\u043E\u0441\u043E\u0431\u0430\u043C\u0438, \u044F\u043A\u0456 \u043D\u0435\u043C\u043E\u0436\u043B\u0438\u0432\u0456 \u043F\u0440\u0438 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0456\u0439 (\u0430\u043D\u0430\u043B\u043E\u0433\u043E\u0432\u0456\u0439) \u043E\u0431\u0440\u043E\u0431\u0446\u0456."@uk , "In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle. The DFT is the most important discrete transform, used to perform Fourier analysis in many practical applications. In digital signal processing, the function is any quantity or signal that varies over time, such as the pressure of a sound wave, a radio signal, or daily temperature readings, sampled over a finite time interval (often defined by a window function). In image processing, the samples can be the values of pixels along a row or column of a raster image. The DFT is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers. Since it deals with a finite amount of data, it can be implemented in computers by numerical algorithms or even dedicated hardware. These implementations usually employ efficient fast Fourier transform (FFT) algorithms; so much so that the terms \"FFT\" and \"DFT\" are often used interchangeably. Prior to its current usage, the \"FFT\" initialism may have also been used for the ambiguous term \"finite Fourier transform\"."@en , "In matematica, in particolare nell'analisi di Fourier, la trasformata discreta di Fourier, anche detta DFT (acronimo del termine inglese Discrete Fourier Transform), \u00E8 un particolare tipo di trasformata di Fourier. Si tratta anche di un caso particolare della trasformata zeta. Si tratta di una trasformata che converte una collezione finita di campioni equispaziati di una funzione in una collezione di coefficienti di una combinazione lineare di sinusoidi complesse, ordinate al crescere della frequenza. Analogamente alla trasformata di Fourier, si tratta di un modo per rappresentare una funzione (la cui variabile \u00E8 spesso il tempo) nel dominio delle frequenze. Le frequenze delle sinusoidi della combinazione lineare (periodica) prodotta dalla trasformata sono multipli interi di una frequenza fondamentale, il cui periodo \u00E8 la lunghezza dell'intero intervallo di campionamento, la durata del segnale. Si differenzia dalla trasformata di Fourier a tempo discreto per il fatto che la funzione in ingresso e la funzione prodotta sono successioni finite, e pu\u00F2 essere quindi considerata come una trasformata per l'analisi di Fourier di funzioni su un dominio limitato e discreto. Diversamente dalla trasformata continua di Fourier, pertanto, la DFT richiede in ingresso una funzione discreta i cui valori sono in generale complessi e non nulli, e hanno una durata limitata. Questo rende la DFT ideale per l'elaborazione di informazioni su un elaboratore elettronico. In particolare la trasformata discreta di Fourier \u00E8 ampiamente utilizzata nel campo dell'elaborazione numerica dei segnali e nei campi correlati per analizzare le frequenze contenute in un segnale, per risolvere equazioni differenziali alle derivate parziali e per compiere altre operazioni, come la convoluzione o la moltiplicazione di numeri interi molto grandi. Alla base di questi utilizzi c'\u00E8 la possibilit\u00E0 di calcolare in modo efficiente la DFT usando gli algoritmi per trasformata di Fourier veloce."@it , "Dyskretna transformata Fouriera (ang. Discrete Fourier Transform, DFT) \u2013 transformata Fouriera wyznaczona dla sygna\u0142u pr\u00F3bkowanego, a wi\u0119c dyskretnego."@pl , "\u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\uFF08\u308A\u3055\u3093\u30D5\u30FC\u30EA\u30A8\u3078\u3093\u304B\u3093\u3001\u82F1\u8A9E: discrete Fourier transform\u3001DFT\uFF09\u3068\u306F\u6B21\u5F0F\u3067\u5B9A\u7FA9\u3055\u308C\u308B\u5909\u63DB\u3067\u3001\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u306B\u985E\u4F3C\u3057\u305F\u3082\u306E\u3067\u3042\u308A\u3001\u4FE1\u53F7\u51E6\u7406\u306A\u3069\u3067\u96E2\u6563\u5316\u3055\u308C\u305F\u30C7\u30B8\u30BF\u30EB\u4FE1\u53F7\u306E\u5468\u6CE2\u6570\u89E3\u6790\u306A\u3069\u306B\u3088\u304F\u4F7F\u308F\u308C\u308B\u3002\u307E\u305F\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3084\u7573\u307F\u8FBC\u307F\u7A4D\u5206\u306E\u6570\u5024\u8A08\u7B97\u3092\u52B9\u7387\u7684\u306B\u884C\u3046\u305F\u3081\u306B\u3082\u4F7F\u308F\u308C\u308B\u3002\u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u306F\uFF08\u8A08\u7B97\u6A5F\u4E0A\u3067\uFF09\u9AD8\u901F\u30D5\u30FC\u30EA\u30A8\u5909\u63DB(FFT)\u3092\u4F7F\u3063\u3066\u9AD8\u901F\u306B\u8A08\u7B97\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\u3068\u306F\u3001\u8907\u7D20\u95A2\u6570 \u3092\u8907\u7D20\u95A2\u6570\u306B\u5199\u3059\u5199\u50CF\u3067\u3042\u3063\u3066\u3001\u6B21\u306E\u5F0F\u3067\u5B9A\u7FA9\u3055\u308C\u308B\u3082\u306E\u3092\u8A00\u3046\u3002 \u3053\u3053\u3067\u3001N\u306F\u4EFB\u610F\u306E\u81EA\u7136\u6570\u3001 \u306F\u30CD\u30A4\u30D4\u30A2\u6570\u3001 \u306F\u865A\u6570\u5358\u4F4D\u3067\u3001\u306F\u5186\u5468\u7387\u3067\u3042\u308B\u3002\u3053\u306E\u3068\u304D\u3001{}\u3092\u6A19\u672C\u70B9\u3068\u3044\u3046\u3002\u307E\u305F\u3001\u3053\u306E\u5909\u63DB\u3092 \u3068\u3044\u3046\u8A18\u53F7\u3067\u8868\u3057\u3001 \u306E\u3088\u3046\u306B\u7565\u8A18\u3059\u308B\u3053\u3068\u304C\u591A\u3044\u3002 \u3053\u306E\u9006\u5909\u63DB\u306B\u3042\u305F\u308B\u9006\u96E2\u6563\u30D5\u30FC\u30EA\u30A8\u5909\u63DB\uFF08\u82F1\u8A9E: inverse discrete Fourier transform\u3001IDFT\uFF09\u306F \u6B63\u898F\u5316\u4FC2\u6570\uFF08DFT \u306F 1, IDFT \u306F 1/N\uFF09\u3084\u6307\u6570\u306E\u7B26\u53F7\u306F\u5358\u306A\u308B\u6163\u7FD2\u7684\u306A\u3082\u306E\u3067\u3042\u308A\u3001\u4E0A\u5F0F\u3068\u306F\u7570\u306A\u308B\u5F0F\u3092\u6271\u3046\u3053\u3068\u304C\u3042\u308B\u3002DFT \u3068 IDFT \u306E\u5DEE\u306B\u3064\u3044\u3066\u3001\u305D\u308C\u305E\u308C\u306E\u6B63\u898F\u5316\u4FC2\u6570\u3092\u639B\u3051\u308B\u3068 1 / N \u306B\u306A\u308B\u3053\u3068\u3068\u3001\u6307\u6570\u306E\u7B26\u53F7\u304C\u7570\u7B26\u53F7\u3067\u3042\u308B\u3068\u3044\u3046\u3053\u3068\u304C\u3060\u3051\u304C\u91CD\u8981\u3067\u3042\u308A\u3001\u6839\u672C\u7684\u306B\u306F\u540C\u4E00\u306E\u5909\u63DB\u4F5C\u7528\u7D20\u3068\u8003\u3048\u3089\u308C\u308B\u3002DFT \u3068 IDFT \u306E\u6B63\u898F\u5316\u4FC2\u6570\u3092\u4E21\u65B9\u3068\u3082 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"In de wiskunde is de discrete fouriertransformatie of DFT een fouriertransformatie die veel wordt toegepast in de digitale signaalverwerking en verwante vakgebieden voor het analyseren van de frequenties die aanwezig zijn in een bemonsterd signaal, en voor het uitvoeren van bewerkingen zoals discrete convoluties. De DFT kan effici\u00EBnt worden berekend door gebruik te maken van het FFT-algoritme. De discrete fouriertransformatie, aangeduid met , is een lineaire transformatie en een discrete vorm van de fouriertransformatie. Ze transformeert een periodieke (periode ) en discrete rij van getallen in een eveneens periodieke discrete rij. De rij van complexe getallen wordt door de DFT getransformeerd in de rij van complexe getallen volgens de formule: en Hierin is de basis van de natuurlijke logaritme, de imaginaire eenheid, en het getal pi. De transformatie wordt ook wel genoteerd als , zoals in . De inverse discrete fouriertransformatie (IDFT) wordt gegeven door Merk op dat de normalisatiefactor die gebruikt wordt in de DFT en IDFT (hier 1 en 1/n) en de tekens van de exponenten slechts conventies zijn, waar vaak van wordt afgeweken. De enige harde eisen bij deze conventies zijn dat de DFT en IDFT exponenten met tegengesteld teken moeten hebben, en dat het product van de beide normalisatie-factoren 1/n moet zijn. Een normalisatiefactor van voor zowel DFT als IDFT maakt de transformaties unitair, hetgeen enkele theoretische voordelen biedt, maar vaak is het praktischer om de schaling van bovenstaande definities aan te houden."@nl , "Diskret fouriertransform, p\u00E5 engelska discrete Fourier transform (DFT), \u00E4r inom matematiken en specifik typ av diskret transform som anv\u00E4nds i fourieranalys. Den transformerar en funktion till en annan som kallas frekvensdom\u00E4ns-representation, eller helt enkelt DFT, fr\u00E5n originalfunktionen, som ofta \u00E4r en funktion i tidsdom\u00E4nen."@sv , "Die Diskrete Fourier-Transformation (DFT) ist eine Transformation aus dem Bereich der Fourier-Analysis.Sie bildet ein zeitdiskretes endliches Signal, das periodisch fortgesetzt wird, auf ein diskretes, periodisches Frequenzspektrum ab, das auch als Bildbereich bezeichnet wird. Die DFT besitzt in der digitalen Signalverarbeitung zur Signalanalyse gro\u00DFe Bedeutung. Hier werden optimierte Varianten in Form der schnellen Fourier-Transformation (englisch fast Fourier transform, FFT) und ihrer Inversen angewandt. Die DFT wird in der Signalverarbeitung f\u00FCr viele Aufgaben verwendet, so z. B. \n* zur Bestimmung der in einem abgetasteten Signal haupts\u00E4chlich vorkommenden Frequenzen, \n* zur Bestimmung der Amplituden und der zugeh\u00F6rigen Phasenlage zu diesen Frequenzen, \n* zur Implementierung digitaler Filter mit gro\u00DFen Filterl\u00E4ngen. Mit der inversen DFT, kurz iDFT kann aus den Frequenzanteilen das Signal im Zeitbereich rekonstruiert werden. Durch Kopplung von DFT und iDFT kann ein Signal im Frequenzbereich manipuliert werden, wie es beim Equalizer angewandt wird. Die Diskrete Fourier-Transformation ist von der verwandten Fouriertransformation f\u00FCr zeitdiskrete Signale (englisch discrete-time Fourier transform, DTFT) zu unterscheiden, die aus zeitdiskreten Signalen ein kontinuierliches Frequenzspektrum bildet."@de , "\u79BB\u6563\u5085\u91CC\u53F6\u53D8\u6362\uFF08Discrete Fourier Transform\uFF0C\u7F29\u5199\u4E3ADFT\uFF09\uFF0C\u662F\u5085\u91CC\u53F6\u53D8\u6362\u5728\u65F6\u57DF\u548C\u9891\u57DF\u4E0A\u90FD\u5448\u79BB\u6563\u7684\u5F62\u5F0F\uFF0C\u5C06\u4FE1\u53F7\u7684\u65F6\u57DF\u91C7\u6837\u53D8\u6362\u4E3A\u5176DTFT\u7684\u9891\u57DF\u91C7\u6837\u3002 \u5728\u5F62\u5F0F\u4E0A\uFF0C\u53D8\u6362\u4E24\u7AEF\uFF08\u65F6\u57DF\u548C\u9891\u57DF\u4E0A\uFF09\u7684\u5E8F\u5217\u662F\u6709\u9650\u957F\u7684\uFF0C\u800C\u5B9E\u9645\u4E0A\u8FD9\u4E24\u7EC4\u5E8F\u5217\u90FD\u5E94\u5F53\u88AB\u8BA4\u4E3A\u662F\u79BB\u6563\u5468\u671F\u4FE1\u53F7\u7684\u4E3B\u503C\u5E8F\u5217\u3002\u5373\u4F7F\u5BF9\u6709\u9650\u957F\u7684\u79BB\u6563\u4FE1\u53F7\u4F5CDFT\uFF0C\u4E5F\u5E94\u5F53\u5C06\u5176\u770B\u4F5C\u5176\u5468\u671F\u5EF6\u62D3\u7684\u53D8\u6362\u3002\u5728\u5B9E\u9645\u5E94\u7528\u4E2D\u901A\u5E38\u91C7\u7528\u5FEB\u901F\u5085\u91CC\u53F6\u53D8\u6362\u8BA1\u7B97DFT\u3002"@zh , "En matem\u00E1ticas, la transformada discreta de Fourier o DFT (del ingl\u00E9s, discrete Fourier transform) es un tipo de utilizada en el an\u00E1lisis de Fourier. Transforma una funci\u00F3n matem\u00E1tica en otra, obteniendo una representaci\u00F3n en el dominio de la frecuencia, siendo la funci\u00F3n original una funci\u00F3n en el dominio del tiempo. Pero la DFT requiere que la funci\u00F3n de entrada sea una secuencia discreta y de duraci\u00F3n finita. Dichas secuencias se suelen generar a partir del muestreo de una funci\u00F3n continua, como puede ser la voz humana. Al contrario que la (DTFT), esta transformaci\u00F3n \u00FAnicamente eval\u00FAa suficientes componentes frecuenciales para reconstruir el segmento finito que se analiza. Utilizar la DFT implica que el segmento que se analiza es un \u00FAnico per\u00EDodo de una se\u00F1al peri\u00F3dica que se extiende de forma infinita; si esto no se cumple, se debe utilizar una ventana para reducir los espurios del espectro. Por la misma raz\u00F3n, la DFT inversa (IDFT) no puede reproducir el dominio del tiempo completo, a no ser que la entrada sea peri\u00F3dica indefinidamente. Por estas razones, se dice que la DFT es una transformada de Fourier para an\u00E1lisis de se\u00F1ales de tiempo discreto y dominio finito. Las funciones sinusoidales base que surgen de la descomposici\u00F3n tienen las mismas propiedades. La entrada de la DFT es una secuencia finita de n\u00FAmeros reales o complejos, de modo que es ideal para procesar informaci\u00F3n almacenada en soportes digitales. En particular, la DFT se utiliza com\u00FAnmente en procesado digital de se\u00F1ales y otros campos relacionados dedicados a analizar las frecuencias que contiene una se\u00F1al muestreada, tambi\u00E9n para resolver ecuaciones diferenciales parciales, y para llevar a cabo operaciones como convoluciones o multiplicaciones de grandes n\u00FAmeros enteros. Un factor muy importante para este tipo de aplicaciones es que la DFT puede ser calculada de forma eficiente en la pr\u00E1ctica utilizando el algoritmo de la transformada r\u00E1pida de Fourier o FFT (Fast Fourier Transform). Los algoritmos FFT se utilizan tan habitualmente para calcular DFTs que el t\u00E9rmino \"FFT\" muchas veces se utiliza en lugar de \"DFT\" en lenguaje coloquial. Formalmente, hay una diferencia clara: \"DFT\" hace alusi\u00F3n a una transformaci\u00F3n o funci\u00F3n matem\u00E1tica, independientemente de c\u00F3mo se calcule, mientras que \"FFT\" se refiere a una familia espec\u00EDfica de algoritmos para calcular DFTs."@es ; dbp:backgroundColour "#F5FFFA"@en ; dbp:borderColour "#0073CF"@en ; dbp:cellpadding 6 ; dbp:indent ":"@en . @prefix prov: . dbr:Discrete_Fourier_transform prov:wasDerivedFrom ; dbo:wikiPageLength "69138"^^xsd:nonNegativeInteger . @prefix wikipedia-en: . dbr:Discrete_Fourier_transform foaf:isPrimaryTopicOf wikipedia-en:Discrete_Fourier_transform .