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  2. 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.

  3. Discrete Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Discrete_Fourier_transform

    The DFT is used in the Fourier analysis of many practical applications. [2] 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 [3]).

  4. Butterfly diagram - Wikipedia

    en.wikipedia.org/wiki/Butterfly_diagram

    A decimation-in-time radix-2 FFT breaks a length-N DFT into two length-N/2 DFTs followed by a combining stage consisting of many butterfly operations. More specifically, a radix-2 decimation-in-time FFT algorithm on n = 2 p inputs with respect to a primitive n -th root of unity ω n k = e − 2 π i k n {\displaystyle \omega _{n}^{k}=e^{-{\frac ...

  5. Fast Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Fast_Fourier_transform

    The development of fast algorithms for DFT can be traced to Carl Friedrich Gauss's unpublished 1805 work on the orbits of asteroids Pallas and Juno.Gauss wanted to interpolate the orbits from sample observations; [6] [7] his method was very similar to the one that would be published in 1965 by James Cooley and John Tukey, who are generally credited for the invention of the modern generic FFT ...

  6. DFT matrix - Wikipedia

    en.wikipedia.org/wiki/DFT_matrix

    An N-point DFT is expressed as the multiplication =, where is the original input signal, is the N-by-N square DFT matrix, and is the DFT of the signal. The transformation matrix W {\displaystyle W} can be defined as W = ( ω j k N ) j , k = 0 , … , N − 1 {\displaystyle W=\left({\frac {\omega ^{jk}}{\sqrt {N}}}\right)_{j,k=0,\ldots ,N-1 ...

  7. Overlap–save method - Wikipedia

    en.wikipedia.org/wiki/Overlap–save_method

    where:. DFT N and IDFT N refer to the Discrete Fourier transform and its inverse, evaluated over N discrete points, and; L is customarily chosen such that N = L+M-1 is an integer power-of-2, and the transforms are implemented with the FFT algorithm, for efficiency.

  8. Chirp Z-transform - Wikipedia

    en.wikipedia.org/wiki/Chirp_Z-transform

    (The other algorithm for FFTs of prime sizes, Rader's algorithm, also works by rewriting the DFT as a convolution.) It was conceived in 1968 by Leo Bluestein. [7] Bluestein's algorithm can be used to compute more general transforms than the DFT, based on the (unilateral) z-transform (Rabiner et al., 1969). Recall that the DFT is defined by the ...

  9. Category:Digital signal processing - Wikipedia

    en.wikipedia.org/wiki/Category:Digital_signal...

    Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. DSP and analog signal processing are subsets of signal processing . It has three major subfields: audio signal processing , digital image processing and speech processing .