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MODIFICATION OF BILINEAR TRANSFORMATION METHOD AND ITS APPLICATION TO DIGITAL FILTERS SYNTHESIS
Vitaly B. Kreyndelin, Moscow Technical University of Communications and Informatics, Moscow, Russia, vitkrend@gmail.com
Elena D. Grigorieva, Moscow Technical University of Communications and Informatics, Moscow, Russia, ed.grigorieva@yandex.ru
Abstract
A generalization of the known method of bilinear transformation for the synthesis of digital filters with infinite impulse response is considered. The application of this generalization avoids the introduction of the pre-emphasis of the frequency scale. Digital filtering is widely used in the development of various devices and systems of information transmission. Often, digital filters have very strict requirements regarding the accuracy of the implementation of the required amplitude-frequency response. The synthesis of digital filters with infinite impulse response uses the known bilinear transformation [1], [2]. However, when using the bilinear transformation, the amplitude-frequency characteristic of the synthesized digital filter does not coincide with the characteristic of the analog filter prototype. Traditionally, to achieve an acceptable correspondence between the characteristics of the prototype filter and the digital filter synthesized on its basis, the pre-selection method is used [2], [6]. Unfortunately, the introduction of the pre-emphasis of the frequency scale in some cases does not allow to achieve the required degree of correspondence between the frequency characteristics of the prototype filter and the digital filter. In this article, we propose an approach to the synthesis of digital filters to avoid the use of the pre-emphasis of the frequency scale, which allows us to implement precision filters with the required frequency response. This approach is based on an extended bilinear transformation. Application of this extended bilinear transformation allows to implement precision filters with the required frequency response.
Keywords: bilinear transformation method, synthesis of filters with infinite impulse response, the pre-emphasis of the frequency scale,
extended bilinear transformation, precision filters.
References
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Information about authors:
Vitaly B. Kreyndelin, Moscow Technical University of Communications and Informatics, chief of department, Moscow, Russia,
Elena D. Grigorieva, Moscow Technical University of Communications and Informatics, deputy chief of department, Moscow, Russia