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- Discrete_Fourier_series abstract "A Fourier series is a representation of a function in terms of a summation of an infinite number of harmonically-related sinusoids with different amplitudes and phases. The amplitude and phase of a sinusoid can be combined into a single complex number, called a Fourier coefficient. The Fourier series is a periodic function. So it cannot represent any arbitrary function. It can represent either:(a) a periodic function, or(b) a function that is defined only over a finite-length interval; the values produced by the Fourier series outside the finite interval are irrelevant.When the function being represented, whether finite-length or periodic, is discrete, the Fourier series coefficients are periodic, and can therefore be described by a finite set of complex numbers. That set is called a discrete Fourier transform (DFT), which is subsequently an overloaded term, because we don't know whether its (periodic) inverse transform is valid over a finite or an infinite interval. The term discrete Fourier series (DFS) is intended for use instead of DFT when the original function is periodic, defined over an infinite interval. DFT would then unambiguously imply only a transform whose inverse is valid over a finite interval. But we must again note that a Fourier series is a time-domain representation, not a frequency domain transform. So DFS is a potentially confusing substitute for DFT. A more technically valid description would be DFS coefficients.".
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- Discrete_Fourier_series wikiPageLength "2301".
- Discrete_Fourier_series wikiPageOutDegree "17".
- Discrete_Fourier_series wikiPageRevisionID "628934463".
- Discrete_Fourier_series wikiPageWikiLink Analog_signal_processing.
- Discrete_Fourier_series wikiPageWikiLink Category:Fourier_analysis.
- Discrete_Fourier_series wikiPageWikiLink DFT_matrix.
- Discrete_Fourier_series wikiPageWikiLink Discrete-time_Fourier_transform.
- Discrete_Fourier_series wikiPageWikiLink Discrete-time_signal.
- Discrete_Fourier_series wikiPageWikiLink Discrete_Fourier_transform.
- Discrete_Fourier_series wikiPageWikiLink Discrete_signal.
- Discrete_Fourier_series wikiPageWikiLink Fast_Fourier_transform.
- Discrete_Fourier_series wikiPageWikiLink Fourier_series.
- Discrete_Fourier_series wikiPageWikiLink Fourier_sine_transform.
- Discrete_Fourier_series wikiPageWikiLink Fractional_Fourier_transform.
- Discrete_Fourier_series wikiPageWikiLink Hwei_P._Hsu.
- Discrete_Fourier_series wikiPageWikiLink Laplace_transform.
- Discrete_Fourier_series wikiPageWikiLink Linear_canonical_transform.
- Discrete_Fourier_series wikiPageWikiLink Linear_canonical_transformation.
- Discrete_Fourier_series wikiPageWikiLink Monson_H._Hayes.
- Discrete_Fourier_series wikiPageWikiLink Short-time_Fourier_transform.
- Discrete_Fourier_series wikiPageWikiLink Sine_and_cosine_transforms.
- Discrete_Fourier_series wikiPageWikiLink Transform_(mathematics).
- Discrete_Fourier_series wikiPageWikiLink Transformation_(function).
- Discrete_Fourier_series wikiPageWikiLinkText "Discrete Fourier series".
- Discrete_Fourier_series hasPhotoCollection Discrete_Fourier_series.
- Discrete_Fourier_series wikiPageUsesTemplate Template:Citation.
- Discrete_Fourier_series wikiPageUsesTemplate Template:Colbegin.
- Discrete_Fourier_series wikiPageUsesTemplate Template:Colend.
- Discrete_Fourier_series subject Category:Fourier_analysis.
- Discrete_Fourier_series hypernym Representation.
- Discrete_Fourier_series comment "A Fourier series is a representation of a function in terms of a summation of an infinite number of harmonically-related sinusoids with different amplitudes and phases. The amplitude and phase of a sinusoid can be combined into a single complex number, called a Fourier coefficient. The Fourier series is a periodic function. So it cannot represent any arbitrary function.".
- Discrete_Fourier_series label "Discrete Fourier series".
- Discrete_Fourier_series sameAs m.09v0x70.
- Discrete_Fourier_series sameAs Q5282035.
- Discrete_Fourier_series sameAs Q5282035.
- Discrete_Fourier_series wasDerivedFrom Discrete_Fourier_series?oldid=628934463.
- Discrete_Fourier_series isPrimaryTopicOf Discrete_Fourier_series.