Walsh - Hadamard Transformation of a Convolution

Abstract

A convolution is mathematical operation used in signal processing, in the homomorphous signal processing and digital image processing (e.g. image interpolation). In regard of computational complexity of the convolution in the time domain, it used to calculate in the other domain. Exp. x(n) * h(n) R X(W) × H(W), resp. X(W) × H(W), shows that a convolution in the time domain corresponds to multiplication in the Z domain, respectively frequency domain. This paper shows utilization of Walsh-Hadamard orthogonal transformations for convolution.