Designing Efficient Bilinear Bicomplex Orthogonal Digital Filters

In this paper a new procedure to design orthogonal digital filters with bicomplex coefficients and a canonical number of elements is developed and tested. The procedure is based on the complex orthogonal transformation, suggested by Watanabe and Nishihara, and permits any real or complex orthogonal transfer function to be transformed into a bicomplex orthogonal one. Unlike the ones offered in literature so far, the new procedure for designing bicomplex orthogonal filters is universally applicable and is not affected by the type or order of the real DSP algorithm used. The main advantage of bicomplex filters is a several times lower order provision. Hence, bilinear bicomplex orthogonal transfer functions are composed of fourth-order real coefficient ones and in this way the filter order is reduced by a factor of four. It is experimentally shown that bicomplex orthogonal filters acquire the properties of the prototype filter, regardless of whether they are real or complex.