Optimal and Suboptimal Error Spectrum Shaping for Cascade-Form Digital Filters

William E. Higgins; David C. Munson

doi:10.1109/TCS.1984.1085528

Optimal and Suboptimal Error Spectrum Shaping for Cascade-Form Digital Filters

William E. Higgins
, David C. Munson

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

Error spectrum shaping (ESS) can significantly reduce finite-wordlength error in recursive fixed-point digital filters. Most past work on ESS has focused on second-order filters. In this paper, expressions for the ESS coefficients minimizing the roundoff error are derived for high-order filters composed of cascaded second-order sections. A comparison of the noise gains is made between optimal and suboptimal ESS structures and the section-optimal structure; the ESS structures perform well in comparison. A heuristic section-ordering strategy, based on ideas underlying ESS, is proposed and deemed useful, particularly for elliptic filters.

Original language	English (US)
Pages (from-to)	429-437
Number of pages	9
Journal	IEEE Transactions on Circuits and Systems
Volume	31
Issue number	5
DOIs	https://doi.org/10.1109/TCS.1984.1085528
State	Published - May 1984

All Science Journal Classification (ASJC) codes

General Engineering

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10.1109/TCS.1984.1085528

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abstract = "Error spectrum shaping (ESS) can significantly reduce finite-wordlength error in recursive fixed-point digital filters. Most past work on ESS has focused on second-order filters. In this paper, expressions for the ESS coefficients minimizing the roundoff error are derived for high-order filters composed of cascaded second-order sections. A comparison of the noise gains is made between optimal and suboptimal ESS structures and the section-optimal structure; the ESS structures perform well in comparison. A heuristic section-ordering strategy, based on ideas underlying ESS, is proposed and deemed useful, particularly for elliptic filters.",

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AB - Error spectrum shaping (ESS) can significantly reduce finite-wordlength error in recursive fixed-point digital filters. Most past work on ESS has focused on second-order filters. In this paper, expressions for the ESS coefficients minimizing the roundoff error are derived for high-order filters composed of cascaded second-order sections. A comparison of the noise gains is made between optimal and suboptimal ESS structures and the section-optimal structure; the ESS structures perform well in comparison. A heuristic section-ordering strategy, based on ideas underlying ESS, is proposed and deemed useful, particularly for elliptic filters.

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ER -

Optimal and Suboptimal Error Spectrum Shaping for Cascade-Form Digital Filters

Abstract

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