Coherent States and Wavelet Transforms

Dr. MR Karim

Department of Mathematics
Alabama A&M University

November 7, 2003
202 Madison Hall
2:00 PM (Coffee and Cookies at 1:30)

Abstract

We show how coherent states of different groups are related to wavelet transforms. We use the coherent states of the Poincaré group in 1-space and 1-time dimensions to define a relativistic 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.