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Explicit expression for the characteristic function of generalized legendre filters
Author(s) -
Rakovich B. D.,
Popovich M. V.
Publication year - 1978
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.4490060406
Subject(s) - mathematics , monotonic function , expression (computer science) , magnitude (astronomy) , legendre polynomials , function (biology) , mathematical analysis , square (algebra) , legendre function , passband , band pass filter , computer science , physics , geometry , astronomy , evolutionary biology , optics , biology , programming language
Abstract The explicit formula for the characteristic function of all‐pole lowpass filters with monotonic passband magnitude response is derived. It is shown that the characteristic function of Legendre, Halpern, LSM and other known classes of monotonic magnitude all‐pole filters that are synthesized from the magnitude squared function, can be obtained by assigning different values to a variable parameter in the general expression obtained. The approximation method consists of using a weighted least‐mean‐square norm to minimize the area under the first derivative of the characteristic function.