Error Spectrum Shaping in Two‐Dimensional Separable‐Denominator Digital Filters

Abstract

AbstractIn the implementation of recursive digital filters, the characteristics might be degraded due to finite word length effects. The degradation generates noise at the filter output which is caused by roundoff errors in the product quantization. A technique called error spectrum shaping (ESS) can be applied to suppress the noise. ESS usually relies on the use of feedback of roundoff errors and sometimes their feedforward. In this paper, a technique is developed for ESS in two‐dimensional separable‐denominator digital filters by applying both feedback and feedforward of roundoff errors. A two‐dimensional separable denominator is implemented with the minimum number of delay elements and includes two quantizers. A genetic algorithm is also applied to obtain the suboptimal discrete solution of feedback–feedforward coefficients for the purpose of cost reduction. Finally, a numerical example is given to illustrate the utility of the proposed technique. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(4): 10–19, 2002