Design and realization of FIR and bireciprocal wave digital filters

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Zhang, Yuhong
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This thesis concentrates on two subjects related to wave digital filter design and realization. Jarmasz provided an efficient cascade synthesis algorithm of lossless two-port networks by extracting elementary sections step by step. Following this approach, based on the factorization of the transfer matrix, necessary and sufficient conditions for cascade synthesis of lossless two-port networks from a given canonic set of scattering polynomials is presented. An algorithm to realize a digital filter with ladder structure based on the cascade decomposition and an illustrative example are also provided. Fettweis proposed another approach to the cascade decomposition of lossless two-port networks based on the factorization of the scattering matrix. A proof that this approach can be applied to FIR filters is provided and at the same time a realization structure and an algorithm in a very general form is developed. Several other realization structures and algorithms for FIR filters are derived directly from this general form, including Fettweis' two structures. An analytical formula method and an optimization method for the design of bireciprocal filters are presented. (Abstract shortened by UMI.)