Abstract
In signal analysis based on linear canonical transform (LCT), researchers often seek signal designs that have the greatest concentrations simultaneously in both time and LCT domains. This paper investigates the extent to which a sequence and its LCT can be simultaneously concentrated in their respective domains. Firstly, the most concentration of indexlimited sequences in LCT domain is derived. Then, the most concentration of (a, b, c, d)-bandlimited sequences in time domain is given. It is shown that the discrete generalized prolate spheroidal sequences (DGPSSs), which generalize the discrete prolate spheroidal sequences proposed by Slepian for Fourier transform to LCT, do the best job of simultaneous concentrations in both time and LCT domains. Associated with DGPSSs are certain related functions of frequency in LCT domain, called discrete generalized prolate spheroidal wave functions (DGPSWFs). Some interesting properties of DGPSWFs as well as two relationships between DGPSSs and DGPSWFs are also presented.
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