Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
An Approach to Realizing Linear Phase Filters Based on the Lagrangean B-Filters
Taikyu KIMToshiyuki MAEDATakahisa ONOHaruhisa HUJITA
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1994 Volume 7 Issue 5 Pages 153-159


An approach to improving attenuation cutoffs is proposed to linear phase filters based on the Lagrangean B-filters approximating the ideal low-pass filter. The impulse response of the mth order Lagragean B-filter holds a non-negative even function symmetry, and all its derivatives of order up to (m-1) are continuos. Hence, the B-filters have linear phase properties in nature. The mth order B-filters are connected in parallel in view of more convenient implementations of circuits than conventional cases, and then each peak component of sidelobe spectra standing close by the main lobes of their frequency domains is cancelled out. This can result in sharper attenuation cutoffs than the mth order B-filter. These mth order linear phase filters realized by this method preserve the bandwith and the asymptotic decay rate of the sidelobe envelope in the mth order B-filter. This approach is illustrated by a few numerical examples.

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