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Discrete Fourier series information


In digital signal processing, a Discrete Fourier series (DFS) a Fourier series whose sinusoidal components are functions of discrete time instead of continuous time. A specific example is the inverse discrete Fourier transform (inverse DFT).

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Discrete Fourier series

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digital signal processing, a Discrete Fourier series (DFS) a Fourier series whose sinusoidal components are functions of discrete time instead of continuous...

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Discrete Fourier transform

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In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...

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Fourier analysis

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simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing...

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Regressive discrete Fourier series

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mathematics, the regressive discrete Fourier series (RDFS) is a generalization of the discrete Fourier transform where the Fourier series coefficients are computed...

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Fast Fourier transform

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A Fast Fourier Transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis...

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Fourier series

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A Fourier series (/ˈfʊrieɪ, -iər/) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a...

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Discrete Fourier transform over a ring

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In mathematics, the discrete Fourier transform over a ring generalizes the discrete Fourier transform (DFT), of a function whose values are commonly complex...

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Fourier transform

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Discrete Fourier transform *DFT matrix Fast Fourier transform Fourier integral operator Fourier inversion theorem Fourier multiplier Fourier series Fourier...

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List of Fourier analysis topics

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Multiplier (Fourier analysis) Fourier shell correlation Pinsky phenomenon Generalized Fourier series Regressive discrete Fourier series Gibbs phenomenon Sigma...

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Frequency domain

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frequency domain. A discrete frequency domain is a frequency domain that is discrete rather than continuous. For example, the discrete Fourier transform maps...

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Harmonic analysis

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transform, continuous/periodic–discrete/aperiodic: Fourier series, discrete/aperiodic–continuous/periodic: discrete-time Fourier transform,...

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Fourier transform on finite groups

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the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...

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Discrete wavelet transform

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illustrate the differences and similarities between the discrete wavelet transform with the discrete Fourier transform, consider the DWT and DFT of the following...

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Finite Fourier transform

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mathematics the finite Fourier transform may refer to either another name for discrete-time Fourier transform (DTFT) of a finite-length series.  E.g., F.J.Harris...

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Convolution theorem

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is also P {\displaystyle P} -periodic, and its Fourier series coefficients are given by the discrete convolution of the U {\displaystyle U} and V {\displaystyle...

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Quantum Fourier transform

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computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The...

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Discrete cosine transform

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a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier series...

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Fourier

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the reverse of the Fourier series, a special case of the Z-transform around the unit circle in the complex plane Discrete Fourier transform (DFT), occasionally...

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Discrete sine transform

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In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real...

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Pontryagin duality

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transforms; and Complex-valued functions on a finite abelian group have discrete Fourier transforms, which are functions on the dual group, which is a (non-canonically)...

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DFS

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or searching tree or graph data structures Discrete Fourier series, the discrete version of Fourier series Dynamic frequency scaling, a method for reducing...

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List of things named after Joseph Fourier

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series, see Laplace series Fourier–Legendre series Fourier transform (List of Fourier-related transforms): Discrete-time Fourier transform (DTFT), the...

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