The nonuniform discrete Fourier transform (NDFT) of a sequence ofnlength N is defined as samples of its z-transform evaluated at Nndistinct points located arbitrarily on the z-plane. The NDFT reduces tonthe conventional discrete Fourier transform (DFT) when these points arenlocated on the unit circle at equally spaced angles. The flexibilitynoffered by the NDFT in choosing the sampling points leads to a variablenspectral resolution that can be controlled by the user. The NDFT isnapplied to nonuniform frequency sampling design of 1-D FIR filters. Thisnmethod produces nearly optimal equiripple 1-D filters with greatlynreduced design times as compared with the Parks-McClellan algorithm.nComparisons with filters designed by other methods are presented tondemonstrate the effectiveness of the proposed method
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