Two‐dimensional recursive digital filters with nearly circular‐symmetric magnitude response and approximately linear phase

Lee, Ju-Hong; Yang, Yuan-Hau

doi:10.1002/cta.697

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…Varshney, Gupta, and Visweswaran also used the interpolation method to design new digital differentiators. Some recent publications in this field have also been reported in the literature.…”

Section: Introductionmentioning

confidence: 95%

Design of recursive digital integrators and differentiators using particle swarm optimization

Jalloul

Al-Alaoui

2015

Circuit Theory & Apps

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This paper presents a new method for designing digital recursive integrators and differentiators by using nonlinear stochastic global optimization based on particle swarm optimization (PSO). A modified PSO is used to optimize the unknown coefficients of second-order and third-order recursive integrators in order to obtain a better magnitude response closer to the ideal integrator. The coefficients of the state-of-theart available filters in the literature are chosen as initial points in the PSO process. By choosing a good starting point, convergence to an optimal solution is greatly facilitated. A dynamic modification of the fitness function used in the PSO process leads to the design of a set of digital integrators each optimized for a specific frequency range. Then, second-order and third-order recursive digital differentiators are designed by inverting and stabilizing the transfer functions of the designed recursive integrators. The obtained stabilized differentiators are further optimized using PSO to further improve their performance. The magnitude responses of the designed filters outperform the existing integrators and differentiators.Additionally Al-Alaoui in [2] proposed an approach to design a digital differentiator by inverting the transfer function of an integrator with similar specifications, stabilizing the resulting transfer function, and compensating the resulting change in magnitude because of the stabilization step that consisted of reflecting the resulting poles, the zeros of the integrator, that lie outside the unit circle at a radius r in the z-plane to 1/r. In [3], he obtained a class of second-order integrators and the corresponding differentiators by interpolating the Simpson and the trapezoidal integration rules and inverting the transfer functions of the obtained integrators.Ngo [4] employed Newton-Cotes integration method to design digital integrators. Tseng-Lee [5] used fractional delay to design digital integrators and Pei and Hsu [6] proposed employing fractional delay filters to obtain new differentiators. Gupta, Jain, and Kumar [7-9] developed digital integrators by interpolating some of the popular digital integration techniques. Varshney, Gupta, and Visweswaran [10] also used the interpolation method to design new digital differentiators. Some recent publications [11][12][13][14] in this field have also been reported in the literature.Recursive digital integrator's design can be formulated as an optimization problem where one searches for the optimal vector of filter coefficients to minimize a certain error function between the designed filter and the ideal integrator given by 1/jw. The previously mentioned methods for designing digital integrators suffer from poor accuracy because only a small fraction of the entire set of candidate vectors of filter coefficients is considered and thus are easily trapped into local optima on the error surface. Papamarkos and Chamzas [15] have used linear programming optimization method to propose the design of digital integrators. Lai, Lin, and ...

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Section: Introductionmentioning

confidence: 95%

Design of recursive digital integrators and differentiators using particle swarm optimization

Jalloul

Al-Alaoui

2015

Circuit Theory & Apps

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“…At the same time, it is important to note that a real benefit will be achieved in the case when both of two complementary filters are of interest because only one additional adder is enough to realize the second filter. For that reason and because of their high computational efficiency [13][14][15], both onedimensional and two-dimensional filters still remain in the focus of researchers [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

A New Method for Design of Selective Digital Iir Filters With Arbitrary Phase

2019

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In this paper the design of selective digital filters that consists of a parallel connection of two all-pass sub-filters is presented. The phase of these filters has given an arbitrary shape ϕ(ω) in both pass-band and stop-band. The proposed method allows the calculation of selective filters with elliptic-like magnitude characteristic. Equations given in the paper are general and suitable for design of filters with arbitrary phase. The efficiency of the method is demonstrated on design of filters with piecewise linear and quadratic phases.

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“…In addition to the standard realization structures, selective filters can be implemented as parallel connection of two all‐pass filters . This configuration has many desirable characteristics, such as low sensitivity and computational efficiency , which is the reason why both one‐dimensional and two‐dimensional filters still remain in the focus of researchers. An all‐pass parallel structure also provides opportunity to realize a pair of complementary filters at a low cost.…”

Section: Introductionmentioning

confidence: 99%

Selective digital filters with quadratic phase

Djurić¹,

Stančić

2016

Circuit Theory & Apps

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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.

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Two‐dimensional recursive digital filters with nearly circular‐symmetric magnitude response and approximately linear phase

Cited by 4 publications

References 16 publications

Design of recursive digital integrators and differentiators using particle swarm optimization

Design of recursive digital integrators and differentiators using particle swarm optimization

A New Method for Design of Selective Digital Iir Filters With Arbitrary Phase

Selective digital filters with quadratic phase

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