Calculation of two dimensional number transform-an analytical study

Abstract

The fact that the elements of two dimensional (2D) arrays, processed by a computer, are sampled on space and quantities in the range /spl plusmn/2/sup n/, permits its treatment as elements of integer fields Z/sub m/. Within the limits of this field, an orthogonal set of functions could be build. These functions form a basis of general Fourier-Galois transformations. The features of these transformations are very close to the well known transformation of Fourier, observe the theorem of time-frequency duality and permit realization of error free calculation of spectra. In cases when powers of 2 are used as twiddle factors, this transformation is known as the number theoretic transform (NTT). In order to improve the practical use of the generalized Fourier-Galois transform, for digital signal processing, this paper presents a study of a method for calculating the two dimensional NTT.