This paper discusses algorithms for processing multidimensional signals which are sampled on regular, but nonrectangular sampiing lattices. Such sampling lattices are dictated by some applications and may be chosen for others because of their resulting symmetric responses or computational efficiencies. We show that any operation which can be performed on a rectangular lattice can be performed on any regular periodic lattice, including FIR and IIR filtering, DFT calculation, and decimation and interpolation. This paper also discusses how generalized decimators and interpolators can be used to convert from one sampling lattice to another.

Using a one-dimensional window as a prototype, a two-dimensional window may be formulated having either a square region of support or a circular one. In this paper we compare the effects of using each of these window formulations for 2-D FIR filter design and present formulas for estimating filter order in terms of design specifications, using a Kaiser window as a prototype.

In this paper the Cooley-Tukey fast Fourier transform (FFT) algorithm is generalized to the multidimensional case in a natural way which allows for the evaluation of discrete Fourier transforms of rectangularly or hexagonally sampled signals or of signals which are sampled on an arbitrary periodic grid in either the spatial or Fourier domain. This general algorithm incorporates both the traditional rectangular row-column and vector-radix algorithms as special cases. This FFT algorithm is shown to result from the factorization of an integer matrix; for each factorization of that matrix, a different algorithm can be developed. This paper presents the general algorithm, discusses its computational efficiency, and relates it to existing multi-dimensional FFT algorithms.