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Using least‐mean‐square‐approximation technique in filter design
Author(s) -
Rakovich B. D.
Publication year - 1977
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490050209
Subject(s) - mathematics , butterworth filter , elliptic filter , passband , monotonic function , low pass filter , network synthesis filters , prototype filter , filter (signal processing) , control theory (sociology) , mathematical analysis , band pass filter , computer science , physics , engineering , control (management) , artificial intelligence , optics , computer vision , electronic engineering
The applications of the least‐mean‐square‐approximation technique to filter synthesis are discussed, and explicit expressions for the characteristic function of all‐pole lowpass filters are derived using a weighted least mean‐square error norm. The weight function depends on one variable parameter which controls the shape of the magnitude response both in the passband and in the stopband. It is shown that most of the filter functions in common use are special cases of this approximation procedure, including Legendre monotonic passband filters as a limiting, degenerate case. Also, a useful generalization of Legendre filter functions is proposed.