文件名称：Fractional discreteq -Fourier transforms
文件大小：1.01MB
文件格式：PDF
更新时间：2015-10-29 06:22:05
Fourier transforms
The discrete Fourier transform (DFT) matrix has a manifold of fractionalizations that depend on the choice of its eigenbases. One prominent basis is that of Mehta functions; here we examine a family of fractionalizations of the DFT stemming from q-extensions of this basis. Although closed expressions are given, many results of our analysis derive from numerical computation and display. Thus we suggest that the account of fractional Fourier transformations applied on signals as presented by other authors—typically of a centred rectangle function—may be biased because the support of the function lies in the central part of the domain only. The phase and amplitude of the whole fractional DFT matrices reveal the location of departures from the continuous kernel of the fractional Fourier integral transform, whose phase and constant amplitude are well known.