DocumentCode :
1189888
Title :
Numerical solution of the Lyapunov equation for narrow-band digital filters
Author :
Gerheim, Albert P.
Volume :
31
Issue :
11
fYear :
1984
fDate :
11/1/1984 12:00:00 AM
Firstpage :
991
Lastpage :
992
Abstract :
The quantization noise generated by a digital filter can be analyzed via the solution of the Lyapunov equation K = AKA^{T} + bb^{T} corresponding to the filter\´s state variable description. A method given by Mullis and Roberts [1] for the solution of the Lyapunov equation is noted for its speed of implementation, but its applicability is limited to filters with wide bandwidths because of numerical accuracy. A method of extending this algorithm to narrowband filters is presented. It uses a transformation which was also presented by Mullis and Roberts. The transformation distorts the frequency response of the filters and improves the numerical accuracy of the solution of the Lyapunov equation. The development given here is restricted to low-pass or high-pass filters, but it can be extended to bandpass filters.
Keywords :
Digital filter wordlength effects; Lyapunov matrix equations; Band pass filters; Bandwidth; Digital filters; Eigenvalues and eigenfunctions; Equations; Narrowband; Noise generators; Power system dynamics; Power system stability; Quantization;
fLanguage :
English
Journal_Title :
Circuits and Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
0098-4094
Type :
jour
DOI :
10.1109/TCS.1984.1085442
Filename :
1085442
Link To Document :
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