Efficient Orthogonal Bicomplex Bilinear DSP Algorithm Design

Abstract

The present paper describes the development of a new technique for designing orthogonal bicomplex Digital Signal Processing (DSP) algorithms. In contrast to those previously reported on, this novel method is of universal application while being unaffected by either the type or the order of the real digital processing algorithm employed as a prototype. The proposed technique builds on Watanabe and Nishihara’s complex orthogonal transformation, and converts real or complex orthogonal transfer functions into bicomplex orthogonal ones. In this study, the new technique is applied to the design and testing of orthogonal bilinear bicomplex filters with a canonical number of elements, the main advantage of which is that they are several times lower in order. In this way, bilinear bicomplex orthogonal transfer functions are made up of real coefficient ones of the fourth-order, thereby reducing the order of the filter by a factor of four. The experiments demonstrate that the properties of the prototype filter are acquired by the bicomplex orthogonal filters, irrespective of the prototype being complex or real in nature.