Sensitivity Analysis of the Equivalent Direct Form of IIR Digital Filters

Lesnikov, Vladislav; Naumovich, Tatiana; Chastikov, Alexander

doi:10.1109/ewdts.2018.8524772

Cited by 2 publications

(1 citation statement)

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“…If a cluster combines r submatrices, then r poles of r-th degree correspond to this cluster. For example [38], in the topological matrix (9) there is one cluster that combines four submatrices. Therefore, the degree of all poles of the canonical form of a fourth-order recursive digital filter is four.…”

Section: The Relationship Between the Thin Structure Of The Topolmentioning

confidence: 99%

Synthesis of Recursive Digital Filters with Finite Word Length: Problems and their Solutions

Lesnikov

Naumovich

Chastikov

2019

MES

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Design of recursive digital filters involves sequential execution of the stages of functional and structural synthesis. At the stage of functional synthesis, the zeros and poles of the transfer function are calculated, which satisfy the specification of the requirements for the characteristics of the filter. At the stage of structural synthesis, a block diagram is formed. At this stage, the calculation of the structure coefficients (parametric synthesis) and the quantization of coefficients are performed. With the traditional approach at the stage of functional synthesis, the effects of the finite word length are not taken into account. At the same time, the stage of structural synthesis leads to distortion of the exact value of the coefficients of the digital filter, distortion of the zeros and poles of the digital filter, distortion of the transfer function, and frequency response. Therefore, it is necessary to either increase the bit depth or change the structural scheme. Despite a large number of publications describing the various structures, their applications are limited by the unique calculation method for each structure and by the extremely short range of the structures offered in available developed systems. This paper is an analytical report, which describes a new approach to the synthesis of recursive digital filters with finite word length. Based on the studied number-theoretic nature of zeros and poles of the digital filters with limited word length, it is proposed to finally compute the zeros and poles of the digital filters at the stage of functional synthesis, considering the limitations on the length of the words. The next step of structural synthesis will not distort the results of functional synthesis. The completed studies have shown the connection between the structure of the digital filters and the number-theoretic nature of zeros and poles. It is proposed to generate structural schemes by this nature, based on the revealed algebraic features of the matrix description of structures.

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Section: The Relationship Between the Thin Structure Of The Topolmentioning

confidence: 99%