Publication

Algorithmes de transformations de Fourier et en cosinus mono et bidimensionnels

Martin Vetterli
1985
Journal Articles

Abstract

Cet article présente un algorithme rapide pour le calcul de la transformée de Fourier discrète et de la transformée en cosinus discrète, et ceci lorsque la longueur de la transformation est une puissance de 2. Il atteint le nombre minimal connu d’opérations (multiplications et additions) pour la transformation de Fourier discrète de séquences réelles, complexes, symétriques et antisymétriques, pour la transformation de Fourier discrète impaire ainsi que pour la transformation en cosinus discrète. L’extension au cas bidimensionnel des transformations de Fourier et cosinus discrètes est également présentée.

Official source

https://infoscience.epfl.ch/entities/publication/20e76721-71c2-4392-9501-ec57788a309a

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Martin Vetterli
1985
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/20e76721-71c2-4392-9501-ec57788a309a

About this result

Related concepts (3)

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.

Fourier analysis

In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.

Multiplication algorithm

A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Efficient multiplication algorithms have existed since the advent of the decimal system. If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.