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In signal processing, any periodic function with period P can be represented by a summation of an infinite number of instances of an aperiodic function , that are offset by integer multiples of P. This representation is called periodic summation: The periodic summation of a Dirac delta function is the Dirac comb. Likewise, the periodic summation of an integrable function is its convolution with the Dirac comb.

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rdfs:label	Periodische Fortsetzung (de) Periodic summation (en)
rdfs:comment	In der Mathematik, insbesondere in der Fourier-Analysis, ist die periodische Fortsetzung oder Periodisierung eine Operation, mit der eine Funktion, die nur in einem bestimmten Intervall definiert ist, periodisch wird. Ein Anwendungsfall sind Fourierreihen, die nur für periodische Funktionen definiert sind. Um sie auch für nicht periodische Funktionen anwenden zu können, muss man sie periodisieren. (de) In signal processing, any periodic function with period P can be represented by a summation of an infinite number of instances of an aperiodic function , that are offset by integer multiples of P. This representation is called periodic summation: The periodic summation of a Dirac delta function is the Dirac comb. Likewise, the periodic summation of an integrable function is its convolution with the Dirac comb. (en)
foaf:depiction
dcterms:subject	Signal processing Functions and mappings
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Link from a Wikipage to another Wikipage	Complex number Convolution Circular convolution Equivalence class Signal processing Signal processing Domain of a function Functions and mappings Fourier series Dirac comb Fractional part Quotient space (linear algebra) Dirac delta function Discrete-time Fourier transform Poisson summation formula Real number Continuous Fourier transform Periodic function Integer multiple Integrable function
sameAs	Periodic summation Periodic summation Periodic summation Periodic summation Periodic summation Periodic summation
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thumbnail	wiki-commons:Special:FilePath/Fourier_transform,_Fourier_series,_DTFT,_DFT.svg?width=300
has abstract	In der Mathematik, insbesondere in der Fourier-Analysis, ist die periodische Fortsetzung oder Periodisierung eine Operation, mit der eine Funktion, die nur in einem bestimmten Intervall definiert ist, periodisch wird. Ein Anwendungsfall sind Fourierreihen, die nur für periodische Funktionen definiert sind. Um sie auch für nicht periodische Funktionen anwenden zu können, muss man sie periodisieren. (de) In signal processing, any periodic function with period P can be represented by a summation of an infinite number of instances of an aperiodic function , that are offset by integer multiples of P. This representation is called periodic summation: When is alternatively represented as a complex Fourier series, the Fourier coefficients are proportional to the values (or samples) of the continuous Fourier transform, at intervals of . That identity is a form of the Poisson summation formula. Similarly, a Fourier series whose coefficients are samples of at constant intervals (T) is equivalent to a periodic summation of which is known as a discrete-time Fourier transform. The periodic summation of a Dirac delta function is the Dirac comb. Likewise, the periodic summation of an integrable function is its convolution with the Dirac comb. (en)
prov:wasDerivedFrom	wikipedia-en:Periodic_summation?oldid=1077570098&ns=0
page length (characters) of wiki page	2689 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Periodic_summation
is Link from a Wikipage to another Wikipage of	Cyclostationary process Upsampling Downsampling (signal processing) Convolution Convolution theorem Wrapped distribution Circular convolution Multidimensional sampling Z-transform Fourier analysis Fourier transform Dirac comb Discretization List of Fourier-related transforms Hilbert transform Laplace transform Rectangular function Discrete-time Fourier transform Discrete Fourier series Discrete Fourier transform Poisson summation formula Nyquist–Shannon sampling theorem Periodic function Undersampling
is foaf:primaryTopic of	wikipedia-en:Periodic_summation

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