FIR Filter Design by a z-Transform on a finite Ring

Hideo MURAKAMI  

Publication
IEICE TRANSACTIONS (1976-1990)   Vol.E64   No.3   pp.155-159
Publication Date: 1981/03/25
Online ISSN: 
DOI: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Digital Circuits
Keyword: 


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Summary: 
Filtering techniques on a finite ring are paralleled to the techniques on the usual complex number field. A z-transform is defines over a finite ring which assimilates the complex number field. This z-transform is related to the usual z-transform and shown to have many properties in common. This z-transform can uniquely represent a filter on the finite ring with a given impulse response or frequency sample response function. The z-transform representation enable one to design recursive FIR (Finite Impulse Response) filter on the finite ring by the analogous methods of the usual z-transform. An interesting property of the recursive filter design on the finite ring is that stability problems due to particular design configulations need not to be considered so long as the inputs are limited to a certain value so that the design problem becomes primarily a problem of complexity reduction.