Novel short-time fractional Fourier transform: theory, implementation, and applications

Shi, Jun, Zheng, Jiabin, Liu, Xiaoping, Xiang, Wei, and Zhang, Qinyu (2020) Novel short-time fractional Fourier transform: theory, implementation, and applications. IEEE Transactions on Signal Processing, 68. pp. 3280-3295.

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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.

Item ID: 63789
Item Type: Article (Research - C1)
ISSN: 1941-0476
Keywords: Time-frequency analysis, Fourier transforms, Chirp, Convolution, Laplace equations, Fractional Fourier transform, short-time fractional Fourier transform, time-fractional-frequency analysis, filter banks
Copyright Information: (C) IEEE
Funders: National Natural Science Foundation of China (NNSFC), Natural Science Foundation of Heilongjiang Province (NSFHP), Fundamental Research Funds for the Central Universities (FRFCU)
Projects and Grants: NNSFC 61871153, NNSFC 61421001, NNSFC U1833203, NSFHP QC2018078, FRFCU HIT.NSRIF.2019027
Date Deposited: 15 Jul 2020 07:49
FoR Codes: 40 ENGINEERING > 4006 Communications engineering > 400607 Signal processing @ 100%
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