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Structural Synthesis of Allpass IIR Digital Filters
Authors
	Lesnikov V.A.
	Naumovich T.V.
	Chastikov A.V.
Date of publication
	2022
DOI
	10.31114/2078-7707-2022-4-179-186
Abstract
	One of the important domains of digital signal processing is the development of IIR allpass digital filters that differ in phase response, and the magnitude response of which is constant at all frequencies. This paper is devoted to the extension of the new approach developed by the authors to the synthesis of IIR digital filters with a finite word length to allpass filters. This approach is based on the fact that the finite wordlength is taken into account even before structural synthesis at the stage of calculating zeros and poles. The calculated values of zeros and poles are final. The next stage of structural synthesis does not distort these values. At the stage of structural synthesis, structures are generated. To describe the structure, a matrix of transmission coefficients between nodes is used, which is called a topological matrix in the paper. For a fixed number of nodes, topological matrices are generated. For filters described by these matrices, transfer function formulas are calculated. The coefficients of these transfer functions are functions of the coefficients of the structure. For calculations, the possibilities of symbolic computations of computer algebra systems MATLAB, Octave or Maple are used. The numerator coefficients of the transfer function of such filters are related in a certain way to the denominator coefficients. These relations are used to form an indefinite system of symbolic equations. The solution of these equations allows one to obtain relations that describe the relationship between the elements of the topological matrix, which are the coefficients of the allpass filter.
Keywords
	all-pass IIR digital filters, structural synthesis, finite wordlength, topological matrix, generation of structures.
Library reference
	Lesnikov V.A., Naumovich T.V., Chastikov A.V. Structural Synthesis of Allpass IIR Digital Filters // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2022. Issue 4. P. 179-186. doi:10.31114/2078-7707-2022-4-179-186
URL of paper
	http://www.mes-conference.ru/data/year2022/pdf/D080.pdf