A synthesis of low‐sensitivity digital filters using T‐cascade connections. Extraction of wave digital lattice filter sections

Abstract

Digital filter response is degraded from that desired when the filter is implemented using finite wordlength multipliers. To avoid such degradation, low‐sensitivity filter structures such as wave digital filters (WDF's) often are used. On the other hand, the pipeline processing would be preferable for the high‐speed applications of filters. In general, the pipeline approach is not applicable to WDF's. This paper proposes new low‐sensitivity filter structures which are also suited for the pipeline processing. The fundamental idea to obtain low‐sensitivity structures is to synthesize digital 2‐port circuits with “structurally induced losslessness,” as done by Vaidyanathan and Mitra. The losslessness of a digital 2‐port circuit is characterized by a para‐unitary scattering matrix. WDF's also have this losslessness when they are modeled after reactance filters. The proposed structures are synthesized by factoring such scattering matrices, and constructed using T‐cascade connection of new basic sections, in contrast with the II‐cas‐cade connection used in WDF's and Vaidyana‐than‐Mitra structures. Each section, which is also characterized by a paraunitary scattering matrix, is realized as a lattice WDF. The proposed structures can realize any given transfer function, and if the function has a certain symmetry, they reduce to lattice WDF's.

A synthesis of pipelineable wave digital filters by scattering matrix factorization

“…Until now, a method by factorization of scattering matrices has been proposed [5], but it can realize only the amplitude response of any given transfer function and uses elementary sections with rather complicated structures. Following [5], elementary sections have been modified to simplify their structures [ 6 ] , whereas the class of realizable transfer function is not changed. On the other hand, Wegener has proposed to synthesize WDFs by factorizing analogdomain scattering matrices [7].…”