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Discretization of analogue filters via H ∞ model‐matching theory
Author(s) -
Toivonen H. T.
Publication year - 1992
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480060507
Subject(s) - discretization , minimax , mathematics , digital filter , frequency response , minification , filter (signal processing) , square integrable function , norm (philosophy) , discretization error , control theory (sociology) , algorithm , computer science , mathematical optimization , mathematical analysis , control (management) , artificial intelligence , law , political science , electrical engineering , computer vision , engineering
Approximation of analogue filters by digital filters is performed using H ∞ model‐matching theory. In this approach the input signal is assumed to belong to a frequency‐weighted ball in the Lebesgue space L 2 of continuous square‐integrable signals and a digital filter is designed so as to minimize the norm of the worst error between the outputs of the digital and analogue filters. An analysis of the frequency response shows that if the set of input signals is sufficiently band‐limited, the procedure corresponds to the minimization of a weighted minimax frequency response error criterion. Numerical examples show that the approach offers an efficient procedure for discretizing general multivariable systems.