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Digital Recursive Filter

IP.com Disclosure Number: IPCOM000076618D
Original Publication Date: 1972-Mar-01
Included in the Prior Art Database: 2005-Feb-24
Document File: 2 page(s) / 31K

Publishing Venue

IBM

Related People

Abensour, D: AUTHOR

Abstract

Conventional methods for the realization of a digital filter consist in the approximation of its magnitude characteristic by a limited number of low-order cells. In fact, the desired magnitude characteristic is only approximated by a limited number of cells, chosen so as to minimize an error criterion. A better approximation of this characteristic can be reached by using a method of approximation known in numerical analysis as "continued fractions", and described in a book by H.S. Wall entitled: "Analytic Theory of Continued Fractions", published by D. Van Nostrand Company Inc. Princeton, New Jersey. According to this method, the filter-transfer function in the "z" plane may be approximated by the formula: (Image Omitted)

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Digital Recursive Filter

Conventional methods for the realization of a digital filter consist in the approximation of its magnitude characteristic by a limited number of low-order cells. In fact, the desired magnitude characteristic is only approximated by a limited number of cells, chosen so as to minimize an error criterion. A better approximation of this characteristic can be reached by using a method of approximation known in numerical analysis as "continued fractions", and described in a book by H.S. Wall entitled: "Analytic Theory of Continued Fractions", published by D. Van Nostrand Company Inc. Princeton, New Jersey. According to this method, the filter-transfer function in the "z" plane may be approximated by the formula:

(Image Omitted)

The corresponding filter of the ith order may be implemented by using identical elementary cells having a transfer function hi (z) such that: hi(2)= 1 over 1+ ai z/-1/.

Knowing that z/-1/ represents a one sampling period delay element, the difference equation of the ith cell, used in the nth order filter, is therefore: Yn = Xn - ai.Y(n-1).

Such a cell is implemented as shown on Fig. 1a. The output sample X is fed to the positive input of summing stage Sigma. The output of Sigma is fed to both the output Y of the filter and to the negative input of Sigma through delay element z/-1/ and weighting element ai.

The formula giving the filter-transfer function H(z) will be implemented by placing the (i+1)th cell between points...