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  2. FFTW - Wikipedia

    en.wikipedia.org/wiki/FFTW

    The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology. [2] [3] [4] FFTW is one of the fastest free software implementations of the fast Fourier transform (FFT).

  3. Fast Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Fast_Fourier_transform

    An example FFT algorithm structure, using a decomposition into half-size FFTs A discrete Fourier analysis of a sum of cosine waves at 10, 20, 30, 40, and 50 Hz. A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT).

  4. Sliding DFT - Wikipedia

    en.wikipedia.org/wiki/Sliding_DFT

    In applied mathematics, the sliding discrete Fourier transform is a recursive algorithm to compute successive STFTs of input data frames that are a single sample apart (hopsize − 1). [1] The calculation for the sliding DFT is closely related to Goertzel algorithm .

  5. Prime-factor FFT algorithm - Wikipedia

    en.wikipedia.org/wiki/Prime-factor_FFT_algorithm

    The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete Fourier transform (DFT) of a size N = N 1 N 2 as a two-dimensional N 1 ×N 2 DFT, but only for the case where N 1 and N 2 are relatively prime.

  6. Discrete Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Discrete_Fourier_transform

    The field of digital signal processing relies heavily on operations in the frequency domain (i.e. on the Fourier transform). For example, several lossy image and sound compression methods employ the discrete Fourier transform: the signal is cut into short segments, each is transformed, and then the Fourier coefficients of high frequencies ...

  7. Gerchberg–Saxton algorithm - Wikipedia

    en.wikipedia.org/wiki/Gerchberg–Saxton_algorithm

    The pseudocode below performs the GS algorithm to obtain a phase distribution for the plane "Source", such that its Fourier transform would have the amplitude distribution of the plane "Target". The Gerchberg-Saxton algorithm is one of the most prevalent methods used to create computer-generated holograms .

  8. Goertzel algorithm - Wikipedia

    en.wikipedia.org/wiki/Goertzel_algorithm

    The Goertzel algorithm is a technique in digital signal processing (DSP) for efficient evaluation of the individual terms of the discrete Fourier transform (DFT). It is useful in certain practical applications, such as recognition of dual-tone multi-frequency signaling (DTMF) tones produced by the push buttons of the keypad of a traditional analog telephone.

  9. Fourier series - Wikipedia

    en.wikipedia.org/wiki/Fourier_series

    A Fourier series (/ ˈ f ʊr i eɪ,-i ər / [1]) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. [2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are ...