Digital linear phase notch filter design based on IIR all-pass filter application

Two-channel quadrature mirror filter banks can be efficiently established by the combination of real-valued infinite impulse response all-pass filters without incurring aliasing and magnitude distortions. The design problem of filter banks is therefore to seek for the phase error minimization of the all-pass filter coefficients. In this paper, a neural network-based Lyapunov energy function is used to relate to the objective function of the designed all-pass filter coefficients. Based on the architecture of neural networks and suitable selection of Hopfield-related parameters, the all-pass filter coefficients are obtained when the networks reach convergence. By further using the suitable combination of the designed all-pass filters, the 2-channel quadrature mirror filter banks with perfect reconstruction can be efficiently accomplished. Simulation results indicate that the neural network-based approach has the advantage of satisfactory performance in magnitude and group delay responses in a parallelism manner.KEYWORDS all-pass filters, infinite impulse response, Lyapunov energy function, neural networks, quadrature mirror filter

Section: Design Of Real-valued Iir All-pass Qmf Banks Using Hopfielmentioning

confidence: 99%

Neural network‐based design of 2‐channel quadrature mirror filter banks

Jou

Lin

Chen

2018

“…In case of linear phase filter, one all‐pass filter could be delay line. It has ideal linear phase at all frequencies, so resulting phase error is only due to the other all‐pass filter phase approximation . So, for a given minimal attenuation a min , the allowed phase approximation error has value

ε = 2 italicarcsin ((), 10^{- a_{m i n} / 20})

.…”

Section: Design Approachmentioning

confidence: 99%

Selective digital filters with quadratic phase

Djurić¹,

Stančić

2016

Self Cite

Summary A method for design of a new class of digital infinite impulse response filters realized as parallel connection of two all‐pass filters is presented in this paper. A new approach to approximation of quadratic phase of all‐pass filter at all frequencies is given. Chosen parallel structure offers opportunity for realization of filters with arbitrary shape phase. The presented algorithm is based on all‐pass filter phase approximation. Phases of both all‐pass filters approximate ideal quadratic phase in minimax sense at all frequencies. Such filters can be applied for chirp signal compression or expansion. Magnitude characteristic of described filters is very selective and elliptic‐like. Obtained filters are compared with elliptic filter and group delay corrector in cascade. For the same specifications, much better results are achieved by the proposed filters. Parallel connection of all‐pass filters introduces lower signal delay, and for a given maximal phase, approximation error demands less complex network. Examples to illustrate the proposed method are given. Copyright © 2016 John Wiley & Sons, Ltd.

“…[1][2][3][4][5][6][7][8][9] Realization of notch filter using cascaded second-order sections form structures inevitable leads to uncontrollable passband gains, 2,6 while iterative design methods based on utilization of convex optimization 3,4,9 or genetic algorithms 5 exhibit high complexity especially for a greater number of notch frequencies. [1][2][3][4][5][6][7][8][9] Realization of notch filter using cascaded second-order sections form structures inevitable leads to uncontrollable passband gains, 2,6 while iterative design methods based on utilization of convex optimization 3,4,9 or genetic algorithms 5 exhibit high complexity especially for a greater number of notch frequencies.…”

Section: Introductionmentioning

confidence: 99%

“…There are several approaches to the IIR multiple-notch filter design. [1][2][3][4][5][6][7][8][9] Realization of notch filter using cascaded second-order sections form structures inevitable leads to uncontrollable passband gains, 2,6 while iterative design methods based on utilization of convex optimization 3,4,9 or genetic algorithms 5 exhibit high complexity especially for a greater number of notch frequencies. All-pass-based IIR multiple-notch filter design methods first introduced in Pei and Tseng 1 transform the specifications of multiple-notch filter magnitude response into those of the phase response of a corresponding all-pass filter.…”

Section: Introductionmentioning

confidence: 99%

Noniterative design of IIR multiple‐notch filters with improved passband magnitude response

Nikolić

Krstić²,

Stančić

2018

Self Cite

A noniterative method for the all-pass-based design of infinite impulse response multiple-notch filters is proposed. This method ensures that specifications regarding positions of notch, left-and right-hand cutoff frequencies, are exactly met, leading to a symmetric magnitude response about notch frequencies. Passband magnitude response can be improved by increasing the order of the corresponding all-pass filter. KEYWORDS all-pass filter, IIR filter, multiple-notch filter, passband magnitude response Int J Circ Theor Appl. 2018;46:2561-2567.wileyonlinelibrary.com/journal/cta