Novel short-time fractional Fourier transform: theory, implementation, and applications
Journal Publication ResearchOnline@JCUAbstract
As a generalization of the classical Fourier transform (FT), the fractional Fourier transform (FRFT) has proven to be a powerful tool for signal processing and analysis. However, it is not suitable for processing signals whose fractional frequencies vary with time due to a lack of time localization information. A simple method to overcome this limitation is the short-time FRFT (STFRFT). There exist several different definitions of the STFRFT in the literature. Unfortunately, these existing definitions do not well generalize the classical result of the conventional short-time FT (STFT), which can be interpreted as a bank of FT-domain filters. The objective of this paper is to propose a novel STFRFT that preserves the properties of the conventional STFT and can be implemented easily in terms of FRFT-domain filter banks. We first present the novel STFRFT and then derive its inverse transform and basic properties. The time-fractional-frequency analysis of this transform is also presented. Moreover, the implementation of the proposed STFRFT is discussed. Finally, we provide several applications for the proposed STFRFT.
Journal
IEEE Transactions on Signal Processing
Publication Name
N/A
Volume
68
ISBN/ISSN
1941-0476
Edition
N/A
Issue
N/A
Pages Count
16
Location
N/A
Publisher
Institute of Electrical and Electronics Engineers
Publisher Url
N/A
Publisher Location
N/A
Publish Date
N/A
Url
N/A
Date
N/A
EISSN
N/A
DOI
10.1109/TSP.2020.2992865