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Generalized Parseval’s Theorem on Fractional Fourier Transform for Discrete Signals and Filtering of LFM Signals

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Author(s): Xiaotong Wang | Guanlei Xu | Yue Ma | Lijia Zhou | Longtao Wang

Journal: Journal of Signal and Information Processing
ISSN 2159-4465

Volume: 04;
Issue: 03;
Start page: 274;
Date: 2013;
Original page

Keywords: Discrete Fractional Fourier Transform (DFRFT) | Uncertainty Principle | Frequency-Limiting Operator | Linear Frequency-Modulation (LFM) Signal | Filtering

ABSTRACT
This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filtering, and examples of filtering for LFM signals in FRFT domains are demonstrated to support the derived conclusions.
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