A relativistic windowed Fourier transform

Author

Karim, M.R. ; Ali, S.T. ; Bodruzzaman, M.

Author_Institution

Dept. of Math., Fisk Univ., Nashville, TN, USA

fYear

2000

fDate

2000

Firstpage

253

Lastpage

260

Abstract

Drawing upon some earlier work on coherent states of the Poincare´ group in l-space and l-time dimensions, we use these states to define a relativistic windowed Fourier transform, as relativistic extension of the usual windowed Fourier transform. We discretize the resulting transform and obtain conditions under which the discretized transform can be used to reconstruct arbitrary square integrable functions. We present some numerical and graphical exercises to illustrate the theory, as well as to compare the relativistic windowed Fourier transform with the orthodox windowed Fourier transform

Keywords

discrete Fourier transforms; group theory; relativity; signal reconstruction; Gabor transform; Poincare´ group; Weyl-Heisenberg group; coherent states; discretized transform; orthodox windowed Fourier transform; relativistic windowed Fourier transform; short-time Fourier transform; space dimension; square integrable functions reconstruction; time dimension; Discrete transforms; Engineering drawings; Fourier transforms; Frequency; Hilbert space; Mathematics; Orbits; Signal analysis; Statistics; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Southeastcon 2000. Proceedings of the IEEE

Conference_Location

Nasville, TN

Print_ISBN

0-7803-6312-4

Type

conf

DOI

10.1109/SECON.2000.845572

Filename

845572