An Approach to Realizing Linear Phase Filters Based on the Lagrangean B-Filters

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  • KIM Taikyu
    College of Science and Engineering, A oyama Gakuin University
  • MAEDA Toshiyuki
    College of Science and Engineering, A oyama Gakuin University
  • ONO Takahisa
    College of Science and Engineering, A oyama Gakuin University
  • HUJITA Haruhisa
    College of Science and Engineering, A oyama Gakuin University

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Other Title
  • ラグランジュB-フィルタに基づく直線位相フィルタの一実現法
  • ラグランジュ B フィルタ ニ モトズク チョクセン イソウ フィルタ ノ イ

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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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