Analysis and Minimization of Roundoff Noise for Generalized Direct-Form II Realization of 2-D Separable-Denominator Filters

Takao HINAMOTO  Akimitsu DOI  Wu-Sheng LU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.7   pp.873-884
Publication Date: 2020/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAP1152
Type of Manuscript: PAPER
Category: Digital Signal Processing
generalized direct-form II,  polynomial operator,  realization,  roundoff noise,  2-D separable-denominator digital filter,  

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Based on the concept of polynomial operators, this paper explores generalized direct-form II structure and its state-space realization for two-dimensional separable-denominator digital filters of order (m, n) where a structure with 3(m+n)+mn+1 fixed parameters plus m+n free parameters is introduced and analyzed. An l2-scaling method utilizing different coupling coefficients at different branch nodes to avoid overflow is presented. Expressions of evaluating the roundoff noise for the filter structure as well as its state-space realization are derived and investigated. The availability of the m+n free parameters is shown to be beneficial as the roundoff noise measures can be minimized with respect to these free parameters by means of an exhaustive search over a set with finite number of candidate elements. The important role these parameters can play in the endeavors of roundoff noise reduction is demonstrated by numerical experiments.