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.