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access icon free Design of nearly linear-phase double notch digital filters with close notch frequencies

© The Institution of Engineering and Technology
Received 25/09/2017, Accepted 18/06/2018, Revised 25/04/2018, Published 17/07/2018

In this study, the authors present a new procedure for the synthesis of the nearly linear-phase infinite impulse response (IIR) filters with two close notch frequencies based on all-pass filter application. The filter is obtained using a parallel connection of the delay line and IIR all-pass filter with a piecewise approximately linear phase. The desired magnitude characteristic is achieved by equiripple approximation of the all-pass filter phase. The magnitude characteristic is equiripple in all passbands. The proposed method is also suitable for the synthesis of complementary filters for extraction of the signal components at prescribed frequencies. The initial solution for the arbitrary order of an all-pass filter is proposed, which attains a sufficient number of phase error extrema. All phase error minima and maxima corresponding to the initial solution have almost identical values, excluding the ones near notch frequencies. As a result, the method exhibits fast and strong convergence. The described method can also be applied for the design of multiple notch filters with two very close notch frequencies.

Inspec keywords: linear phase filters; approximation theory; notch filters; IIR filters

Other keywords: multiple notch filters; nearly linear-phase infinite impulse response filters; desired magnitude characteristic; delay line; complementary filter synthesis; equiripple approximation; piecewise approximately linear phase; signal component extraction; nearly linear-phase IIR filters; all phase error maxima; all-pass filter application; IIR all-pass filter; all phase error minima; nearly linear-phase double notch digital filters; close notch frequencies

Subjects: Filtering methods in signal processing; Digital filters; Interpolation and function approximation (numerical analysis); Digital signal processing; Digital filters; Interpolation and function approximation (numerical analysis)

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