Optimum Design of Discrete-Time Differentiators via Semi-Infinite Programming Approach

Ho, Charlotte Yuk-Fan; Ling, Bo; Liu, Yanping; Tam, P.K.S.; Teo, K.L.

doi:10.1109/tim.2008.922090

Cited by 10 publications

(2 citation statements)

References 6 publications

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“…The contribution of this work is to present thoroughly a general and flexible approach for designing optimal filter bank systems for dynamic phasor estimation. It is based on convex semi-infinite programming (CSIP), a powerful tool for optimal digital filter design [15], [16], [17]. Basically, it extends the idea of the work [18] to a filter bank (FB) which provides not only a phasor estimate but also phasor derivative estimates.…”

Section: B Contribution and Challengesmentioning

confidence: 99%

Optimal Differentiator Filter Banks for PMUs and Their Feasibility Limits

Messina

Vega

Marchi

et al. 2017

IEEE Trans. Instrum. Meas.

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In this paper, we present a very general design approach for optimal linear-phase phasor filter bank algorithms for PMUs based on convex semi-infinite optimization. A detailed presentation of the formulation of both the cost functions and constraints is included for the positive-sequence estimation problem. The design method is extremely powerful and flexible as it allows to control precisely the behavior of the system in terms of the total vector error (TVE), frequency error (FE), and rate of change of frequency error (RFE) metrics for several different scenarios. This feature is extremely useful for tailored designs of these filters for different applications. We also determine numerically the uniform feasibility limits of the system as a function of the filter lengths and, in particular, study the required filter lengths for compliance with the IEEE Standards C37.118. 1-2011 and C37.118.1a-2014. It is found that all requirements can be achieved with a significant margin with the exception of the M class FE constraint for interharmonic components, an issue which is also reported in other works and briefly discussed here. Finally, an interesting comparison with the Taylor-Fourier filters is made to illustrate the advantages of our approach.

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Section: B Contribution and Challengesmentioning

confidence: 99%

Optimal Differentiator Filter Banks for PMUs and Their Feasibility Limits

Messina

Vega

Marchi

et al. 2017

IEEE Trans. Instrum. Meas.

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“…The derivative of a digital signal is useful in many signal processing and communication applications which can be conveniently computed using a digital differentiator. Linear phase FIR differentiator design can be formulated as a minimax (MM) problem [1, 2], a least‐squares (LS) problem [3], a weighted least squares (WLS) problem [4], and an eigenfilter problem [5, 6]. The optimisation design of these problems can be performed through mathematical optimisation algorithms and evolutionary optimisation algorithms.…”

Section: Introductionmentioning

confidence: 99%

Design of p ‐norm linear phase FIR differentiators using adaptive modification rate artificial bee colony algorithm

Kwan

Raju

2020

IET signal process.

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In this paper, an adaptive modification rate artificial bee colony (AMR‐ABC) algorithm is proposed by incorporating a novel adaptive modification rate to adaptively balance exploration and exploitation to determine which parameters (or the number of parameters) to be updated in a solution during each iteration. The performance of the AMR‐ABC algorithm is compared to those the standard ABC algorithm and its two variants, and the Parks–McClellan algorithm for designing Type 3 (orders: 14, 26, and 38) and Type 4 (orders: 13, 25, and 37) linear phase FIR differentiators to evaluate their design capabilities. Design results have shown that the proposed AMR‐ABC algorithm (i) outperforms four other design algorithms with the lowest p‐norm error in each of the six differentiator designs and (ii) is robust such that the same p‐norm error solution with an equiripple amplitude response in each of the six differentiator designs can be obtained by repeating a design with a different population of randomly generated initial solutions. The filter coefficients of six linear phase FIR differentiator designs are given as benchmarks to compare the p‐norm error performance of the AMR‐ABC algorithm to other algorithms. The AMR‐ABC algorithm is attractive to be used for optimisation in this and other design problems.

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Specification parameters for finite word length linear‐phase FIR single‐band PCLS filters

Ling

2018

Adaptive Control & Signal

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SummaryFinite word length linear‐phase finite impulse response filters can be implemented using low‐cost devices. Among them, the single‐band peak‐constrained least squares filters are the most common one employed in many engineering applications. To design these filters, it is required to define the specifications on the maximum passband ripple magnitude, the maximum stopband ripple magnitude, and the number of bits for representing the filter coefficients. Most of the existing works on the filter design are on the determination of the filter coefficients based on a given set of these specification parameters. However, very few works are on the determination of these specification parameters. Hence, this paper establishes the analytical relationships among these specification parameters. In particular, the relationship between the total ripple energy and the maximum ripple magnitude of the filter, the relationship between the number of bits for representing the filter coefficients and the total ripple energy of the filter, and the relationship between the number of bits for representing the filter coefficients and the maximum ripple magnitude of the filter are established. Computer numerical simulations are presented for verifying the obtained results.

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Optimum Design of Discrete-Time Differentiators via Semi-Infinite Programming Approach

Cited by 10 publications

References 6 publications

Optimal Differentiator Filter Banks for PMUs and Their Feasibility Limits

Optimal Differentiator Filter Banks for PMUs and Their Feasibility Limits

Design of p ‐norm linear phase FIR differentiators using adaptive modification rate artificial bee colony algorithm

Specification parameters for finite word length linear‐phase FIR single‐band PCLS filters

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