1. INTRODUCTION. Edge detection and the detection of discontinuities are important in many fields. In image processing, for example, one often needs to determine the boundaries of the items of which a picture is composed. (For more information about edge detection in image processing, see [10].) We consider the problem of detecting the edges present in a function when given the Fourier coeffici...

The Fourier transform is an integral part of signal processing of any kind. To be able to analyze an input signal as a superposition of infinitely many signals of different frequency allows for manipulation of the coefficients and, after completing the inverse Fourier transform, interesting effects on the initial signal. Thus, in my project I focused on creating pitch correction effects as seen...

Media forensics tries to determine the originating device of a signal. We apply this paradigm to microphone forensics, determining the microphone model used to record a given audio sample. Our approach is to extract a Fourier coefficient histogram of near-silence segments of the recording as the feature vector and to use machine learning techniques for the classification. Our test goals are to ...

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Michhelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a func...