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The least‐square design of minimum‐order allpass‐based infinite impulse response multi‐notch filters
Author(s) -
Krstić Ivan
Publication year - 2021
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.3100
Subject(s) - mathematics , band stop filter , all pass filter , control theory (sociology) , low pass filter , infinite impulse response , filter design , phase response , impulse response , filter (signal processing) , cutoff frequency , linear filter , finite impulse response , digital filter , mathematical analysis , frequency response , algorithm , computer science , physics , engineering , control (management) , artificial intelligence , electrical engineering , computer vision , optics
Summary The paper investigates the least‐square design of minimum‐order infinite impulse response multi‐notch filters. Monotonically decreasing nature of the stable allpass filter's phase response, characterizing the allpass‐based multi‐notch filter, along with the simple relation between coefficients and the phase response of the allpass filter, allows the formulation of the multi‐notch filter's magnitude response specifications as the linear equality constraints regarding the positions of notch, left‐ and right‐hand cutoff frequencies. Since the number of such constraints equals triple the number of notch frequencies, while the number of unknown filter coefficients equals double the number of notch frequencies, variable elimination is first performed to ensure that specifications regarding the notch frequencies positions are strictly satisfied. The remaining overdetermined system of linear equations is then solved in the least‐square sense, leading to the approximate satisfaction of left‐ and right‐hand cutoff frequencies positions. Proposed design method is also compared with some of the existing infinite impulse response multi‐notch filter design methods.