Synthesis of pipelineable complex wave digital filters

A decomposition algorithm is presented for the synthesis of pipelineable, modular, cascade, complex wave (unitary) digital filters (CWDFs) with emphasis on simplicity of implementation. The main features of the algorithm are the following: (1) the extraction step obviates coefficient-form polynomial manipulations and zero-finding operations by using an alternative representation of the canonic polynomials that describe the lossless two-port; (2) first-order sections that effect pipelineability are treated like any other section (they realize a transmission zero at z^-1=0, thus eliminating the need for special treatment; (3) a fully general first-order complex section is derived that can realize a “transmission zero” anywhere in the z-plane and is the only section required 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^±jw(0) transmission zeros and a 2nd-order real section. Also, a method is presented for investigating coefficient quantization effects directly in the z-domain