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


Durak L.

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, cilt.346, ss.136-146, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 346 Konu: 2
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1016/j.jfranklin.2008.08.006
  • Dergi Adı: JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
  • Sayfa Sayıları: ss.136-146

Özet

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.