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Synthesis of Recursive Digital Filters with Finite Word Length: Problems and Their Solutions
Authors
	Lesnikov V.A.
	Naumovich T.V.
	Chastikov A.V.
Date of publication
	2018
DOI
	10.31114/2078-7707-2018-4-89-97
Abstract
	With the traditional approach to the synthesis of recursive digital filters, it is possible to distinguish such stages as func-tional synthesis, in which the transfer function (its zeros and poles) is calculated, the choice of the structural scheme (struc-tural synthesis), parametric synthesis (calculation of the coef-ficients of the selected structure without taking into account the finite word length), quantization of the coefficients. The last operation results in distortion of the exact value of the coefficients of digital filter, distortion of the zeros and poles of the digital filter, distortion of the transfer function, and fre-quency responce. Further, they resort either to an increase in the digit capacity, or to a change in the structural scheme. Despite the large number of publications describing the vari-ous structures, their application is limited by the uniqueness of the calculation method for each structure, the extremely limited nomenclature of the structures offered in accessible development 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 fil-ters with finite word length, it is proposed to finally compute the zeros and poles of the digital filters at the stage of func-tional synthesis, considering the limitations on the length of the words. The next stage 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 in accordance with this nature, based on the revealed algebraic features of the matrix description of structures.
Keywords
	recursive digital filter, finite word length, algebraic numbers, quantization of coefficients, discretization of the z-plane, to-pography of the z-plane, topological matrix.
Library reference
	Lesnikov V.A., Naumovich T.V., Chastikov A.V. Synthesis of Recursive Digital Filters with Finite Word Length: Problems and Their Solutions // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2018. Issue 4. P. 89-97. doi:10.31114/2078-7707-2018-4-89-97
URL of paper
	http://www.mes-conference.ru/data/year2018/pdf/D102.pdf