This paper describes the theory, simulation, and construction of a two-dimensional number theoretic transform (NTT) convolver. The convolver performs indirect convolution by using the cyclic convolution property of a class of generalized discrete Fourier transforms (DFT's) defined over rings isomorphic to direct sums of Galois fields. The paper first presents the theoretical development of the computational element required for computing the generalized discrete Fourier transform (GDFIT) and its inverse. The theory extends the use of base fields to second degree extension fields and provides efficient choices for transform parameters to minimize hardware. The paper next presents results of recent work in multidimensional transform memory structures, and extends this work to the complete convolution process. The two theories are then "married" to produce efficient, very high speed convolution architectures. Simulation results are presented for a second degree extension field image convolver and constructional details are presented for a fast image convolver using 2 base fields and designed to operate as a peripheral to a fast 32 bit minicomputer.

This paper describes the design of an image convolver suitable for the convolution of a (256 × 256) image with large filter impulse responses in under 1/30 of a second. The memory architecture of the convolver is based on the structures associated with parallel and pipelined FFT/NTT processors that use ROM oriented implementation of the Residue Number System and a 2 D radix-r Ordered-input, Ordered-output FFT algorithm. The 2 D convolution operation is performed by the use of overlap-save technique of sectioned convolutions.