JIAN-JIUN DINGSOO-CHANG PEI2007-04-192018-07-062007-04-192018-07-06200515206149http://scholars.lib.ntu.edu.tw/handle/123456789/317593http://ntur.lib.ntu.edu.tw/bitstream/246246/200704191001471/1/01415984.pdfhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-33646809794&doi=10.1109%2fICASSP.2005.1415984&partnerID=40&md5=e98bae42d82b1020cfcfcb8e0e81f861It 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]SDG7Boundary conditions; Error correction; Estimation; Fourier transforms; Sampling; Band-limited signal; Prolate spheroidal wave functions (PSWF); Sampling theory; Shannon's theory; Signal processingconference paper10.1109/icassp.2005.1415984http://ntur.lib.ntu.edu.tw/bitstream/246246/200704191001471/1/01415984.pdf