Shift-invariance of short-time Fourier transform in fractional Fourier domains


Durak L.

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, vol.346, no.2, pp.136-146, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 346 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.1016/j.jfranklin.2008.08.006
  • Title of Journal : JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
  • Page Numbers: pp.136-146

Abstract

Fractional Fourier domains form a continuum of domains making arbitrary angles with the time or frequency domains on the time-frequency plane. Signal representations in these domains are related to the fractional Fourier transform (FrFT). In this paper, a new proof on the shift-invariance of linear time-frequency distributions on fractional Fourier domains is given. We show that short-time Fourier transform (STFT) is the unique linear distribution satisfying magnitude-wise shift-invariance in the fractional Fourier domains. The magnitude-wise shift-invariance property in arbitrary fractional Fourier domains distinguishes STFT among all linear time-frequency distributions and simplifies the interpretation of the resultant distribution as shown by numerical examples. (C) 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.