Wavelet analysis is a new mathematical technique and in the recent years enormous interest in application of engineering has been observed. This new technique is particularly suitable for non-stationary processes as in contrast to the Fourier transform (FT). The wavelet transform (WT) allows exceptional localization, both in time and frequency domains. The application of the WT to earthquake en...

It is shown in this paper that the discrete equivalent of a chirp filter is needed to implement the computation of the discrete Fourier transform (DFT) as a linear filtering process. We show further that the chirp filter should not be realized as a transversal filter in a wide range of cases; use instead of the conventional FFT permits the computation of the DFT in a time proportional to N logz...

A general approach to arithmetic Fourier transforms is developed. The implementation is based on the concept of killer polynomials and the solution of an arithmetic deconvolution problem pertaining to a generalized Mobius transform. This results in an extension of the Bruns procedure, valid for all prime numbers, and in an AFT that extracts directly the sine coefficients from the Fourier series.

Very broadly speaking, the Fourier transform is a systematic way to decompose “generic” functions into a superposition of “symmetric” functions. These symmetric functions are usually quite explicit (such as a trigonometric function sin(nx) or cos(nx)), and are often associated with physical concepts such as frequency or energy. What “symmetric” means here will be left vague, but it will usually...