Reducing sampling error by prolate spheroidal wave functions and fractional Fourier transform
Journal
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Journal Volume
IV
Pages
IV217-IV220
Date Issued
2005
Author(s)
Abstract
It is known that one can use Shannon's theory to sample a band-limited signal. In this paper, we introduce how to use prolate spheroidal wave functions (PSWFs) to sample a time-limited and nearly band-limited signal. PSWFs have the property of optimal energy concentration. Thus we can apply it for sampling theory to reduce the aliasing error of the recovered signal. We derive the theory that can estimate the upper bound of the error. With it, we can determine that, to achieve certain accuracy, how many samples we should acquire. Moreover, we combine the proposed sampling theory with the fractional Fourier transform (FRFT). We also find an important theory, i.e., to achieve a certain degree of accuracy, the number of sampling points required for a signal is proportional to the 'area' of its time-frequency distribution. © 2005 IEEE.
SDGs
Other Subjects
Boundary conditions; Error correction; Estimation; Fourier transforms; Sampling; Band-limited signal; Prolate spheroidal wave functions (PSWF); Sampling theory; Shannon's theory; Signal processing
Type
conference paper
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