Publication

Simple FFT and DCT algorithms with reduced number of operations

Martin Vetterli
1984
Journal Articles

Abstract

A simple algorithm for the evaluation of discrete Fourier transforms (DFT) and discrete cosine transforms (DCT) is presented. This approach, based on the divide and conquer technique, achieves a substantial decrease in the number of additions when compared to currently used FFT algorithms (30% for a DFT on real data, 15% for a DFT on complex data and 25% for a DCT) and keeps the same number of multiplications as the best known FFT algorithms. The simple structure of the algorithm and the fact that it is best suited for real data (one does not have to take a transform of two real sequences simultaneously anymore) should lead to efficient implementations and to a wide range of applications.

Official source

https://infoscience.epfl.ch/entities/publication/b06ca698-3186-4d6b-840e-ccad2e1d5b49

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Martin Vetterli
1984
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/b06ca698-3186-4d6b-840e-ccad2e1d5b49

About this result

Related concepts (32)

Fast Fourier transform

A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical.

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

Discrete cosine transform

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including (such as JPEG and HEIF), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus).

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Simple FFT and DCT algorithms with reduced number of operations

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