The fast Fourier transform and fast wavelet transform for patterns on the torus
نویسندگان
چکیده
منابع مشابه
Wavelet transform based fast approximate Fourier transform
We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coe cients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational comple...
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The Fourier transform has been used as a reliable tool in signal analysis for many years. Invented in the early 1800s by its namesake, Jean Baptiste Joseph Fourier, the Fourier transform has become a cornerstone of modern signal analysis. The Fourier transform has proven incredibly versatile in applications ranging from patten recognition to image processing. Nevertheless, it suuers from certai...
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Suppose we have a function s(t) that measures the sound level at time t of an analog audio signal. We assume that s(t) is piecewise-continuous and of finite duration: s(t) = 0 when t is outside some interval a ≤ t ≤ b. Make a change of variable x = (t− a)/(b− a) and set f(x) = s(t). Then 0 ≤ x ≤ 1 when a ≤ t ≤ b, and f(x) is a piecewise continuous function of x. We convert f(x) into a digital s...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2013
ISSN: 1063-5203
DOI: 10.1016/j.acha.2012.07.007