SYNTHESIS OF PIPELINEABLE COMPLEX WAVE DIGITAL-FILTERS

A decomposition algorithm is presented for the synthesis of pipelineab le, modular, cascade, complex wave (unitary) digital filters (CWDFs) w ith emphasis on simplicity of implementation. The main features of the algorithm are the following: (1) The extraction step obviates coeffic ient-form polynomial manipulations and zero-finding operations by usin g an alternative representation of the canonic polynomials that descri be the lossless two-port-a method first introduced for real two-port s ynthesis in [1]; (2) First-order sections that effect pipelineability are treated like any other section (they realize a transmission zero a t z-1 = 0), thus eliminating the need for special treatment; (3) A ful ly general first-order complex section is derived that can realize a ' 'transmission zero'' anywhere in the z-plane and is the only section r equired for the cascade decomposition. The algorithm can also be used to synthesize real two-port networks; equivalences are given between a cascade of two complex sections with ke+/-jomega(o) transmission zero s and a 2nd-order real section. Also, a method is presented for invest igating coefficient quantization effects directly in the z-domain.