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# Sensitivity of Pipelined Recursive Digital Filters

IP.com Disclosure Number: IPCOM000061752D
Original Publication Date: 1986-Sep-01
Included in the Prior Art Database: 2005-Mar-09
Document File: 3 page(s) / 27K

IBM

Sinha, B: AUTHOR

## Abstract

A technique is described whereby the sensitivity of a pipelined recursive digital filter, with respect to the coefficient errors, is determined without solving for the location of the poles. Sensitivity of recursive digital filters is the change in the pole location of the filter due to the changes in the coefficient values of the realization. A second order infinite impulse response IIR digital filter may be characterized by the transfer function (Image Omitted) Realizing this with the pipeline technique of k stages of pipeline, the transfer function is augmented by p, where p is a function of k. The augmented transfer function obtained has a general form (Image Omitted) The augmenting process involves multiplying the numerator and the denominator of the original transfer function by the same polynominal.

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Sensitivity of Pipelined Recursive Digital Filters

A technique is described whereby the sensitivity of a pipelined recursive digital filter, with respect to the coefficient errors, is determined without solving for the location of the poles. Sensitivity of recursive digital filters is the change in the pole location of the filter due to the changes in the coefficient values of the realization. A second order infinite impulse response IIR digital filter may be characterized by the transfer function

(Image Omitted)

Realizing this with the pipeline technique of k stages of pipeline, the transfer function is augmented by p, where p is a function of k. The augmented transfer function obtained has a general form

(Image Omitted)

The augmenting process involves multiplying the numerator and the denominator of the original transfer function by the same polynominal. The poles of this realization are a function of b and b . Therefore, the sensitivity is the magnitude of the changes in the pole locations due to errors in these coefficients. The changes in each pole location relative to the parameters may be expressed as follows:

(Image Omitted)

These are the measurements of the sensitivity of the ith pole to an error in the two coefficients and are valid only for simple order poles. Therefore, before a recursive pipeline digital filter is built, it is possible to calculate these values for every pole Zi in the system. The magnitude of the change in pole locations may be derived as

(Image Omitted)

However, with this method, all pole loc...