A relativistic windowed Fourier transform

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.