The nonuniform discrete Fourier transform and its applications infilter design. II. 2-D

摘要

For part I see ibid., vol. 43, no. 6, p. 422-33 (1996). Thenconcept of the nonuniform discrete Fourier transform (NDFT) is extendednto two dimensions to provide a basic framework for nonuniform samplingnof 2-D sequences in the frequency domain. The 2-D NDFT of a sequence ofnsize N1×N2 is defined as samples of its 2-Dnz-transform evaluated at N1N2 distinct pointsnlocated in the 4-D (z1, z2) space. These pointsnare chosen appropriately so that the inverse transform exists. Wendiscuss two special cases in which the choice of the sampling points isnconstrained so that the 2-D NDFT matrix is guaranteed to be nonsingular,nand the number of operations required for computing its inverse isnreduced, The 2-D NDFT is applied to nonuniform frequency sampling designnof 2-D finite-impulse-response (FIR) filters. Nonseparable filters withngood passband shapes and low peak ripples are obtained. This isnillustrated by design examples, in which 2-D filters with various shapesnare designed and compared with those obtained by other existing methods