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S. C. Pei and J. J. Ding, “Eigenfunctions of the Offset Fourier, Fractional Fourier, and Linear Canonical Transforms,” Journal of the Optical Society of America A, Vol. 20, 2003, pp. 522-532. doi:10.1364/JOSAA.20.000522

has been cited by the following article:

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

  AUTHORS: Xiaotong Wang, Guanlei Xu, Yue Ma, Lijia Zhou, Longtao Wang

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

  JOURNAL NAME: Journal of Signal and Information Processing, Vol.4 No.3, August 15, 2013

  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.