| The structural precision of digital filters and the structure of the coefficients of the transfer function denominator |
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| Authors |
| | Lesnikov V.A. |
| | Naumovich T.V. |
| | Chastikov A.V. |
| Date of publication |
| | 2020 |
| DOI |
| | 10.31114/2078-7707-2020-4-217-224 |
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| Abstract |
| | This paper was prepared as part of a project dedicated to the development of a new approach to the synthesis of IIR digital filters with a finite word length. This approach involves taking into account the finite word length already at the stage of calculating zeros and poles even before the stage of structural synthesis. In this case, it is taken into account that the zeros and poles of practically implemented filters are elements of the set of algebraic numbers of the corresponding degree. Next, filter structures with quantized coefficients are generated, during which the calculated values of zeros and poles should not be distorted. This is achieved through the use of previously obtained knowledge about the fine structure of the matrix of transmission coefficients between the nodes of the structural diagram. A method for generating structures is described that takes into account the structural precision of the filter, independent of its specific characteristics. Structural precision is determined by the degree of algebraic numbers, which are the poles of the filter and the structure of the coefficients of the transfer function denominator. Expressions are heuristically obtained that simplify the process of generating structures for some values of the structure dimension (number of nodes). The absence of such expressions in general terms is not an obstacle to solving the problem of structural synthesis. All the necessary information can be obtained using the capabilities of symbolic computing of computer algebra systems Maple and Matlab. Plans for further research involve obtaining new expressions that allow us to generate structures with a given structural precision with-out the need for Maple or Matlab. It is planned to expand the methods of structural synthesis taking into account the structural precision of the zeros of the transfer function. |
| Keywords |
| | IIR digital filters, finite word length, algebraic numbers, structural precision, topological matrix |
| Library reference |
| | Lesnikov V.A., Naumovich T.V., Chastikov A.V. The structural precision of digital filters and the structure of the coefficients of the transfer function denominator // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2020. Issue 4. P. 217-224. doi:10.31114/2078-7707-2020-4-217-224 |
| URL of paper |
| | http://www.mes-conference.ru/data/year2020/pdf/D119.pdf |
