Multiresolution signal processing by Fourier transform time-frequency correlation analysis

Author

Anugom, Julian U. ; Grigoryan, Artyom M.

Author_Institution

The University of Texas at San Antonio, Department of Electrical and Computer Engineering, 6900 North Loop 1604 West, 78249-0669, USA

fYear

2006

fDate

7-9 April 2006

Firstpage

296

Lastpage

301

Abstract

In this paper, multiresolution signal processing is described, by the continuous Fourier transform, not the short-time Fourier transform. The inverse Fourier transform is defined by the integral Fourier formula which is referred to as the correlation of the function (signal) with cosine waveforms of various frequencies. This is a direct way to perform the time-frequency analysis of signals. The Fourier transform is described as the sum of wavelet-like transforms with the cosine analyzing function of one period. Properties of such transforms, including the inverse formula of reconstruction of the signal by the described wavelet-like transforms are described. Examples of application of such transforms to detect the exact location of a high-frequency signal are given.

Keywords

Discrete transforms; Fourier transforms; Image reconstruction; Signal analysis; Signal processing; Signal resolution; Speech analysis; Time frequency analysis; Wavelet analysis; Wavelet transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Region 5 Conference, 2006 IEEE

Conference_Location

San Antonio, TX, USA

Print_ISBN

978-1-4244-0358-5

Electronic_ISBN

978-1-4244-0359-2

Type

conf

DOI

10.1109/TPSD.2006.5507413

Filename

5507413