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

Durak, Lütfiye

doi:10.1016/j.jfranklin.2008.08.006

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

Atıf İçin Kopyala

Durak L.

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, cilt.346, sa.2, ss.136-146, 2009 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 346 Sayı: 2
Basım Tarihi: 2009
Doi Numarası: 10.1016/j.jfranklin.2008.08.006
Dergi Adı: JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.136-146
İstanbul Teknik Üniversitesi Adresli: Hayır

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.