Design of linear-phase IIR filters via impulse-response gramians

Sreeram, Victor; Agathoklis, P.

doi:10.1109/78.124948

Cited by 53 publications

(42 citation statements)

References 13 publications

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“…In fact, Li and colleagues [6] have shown that the method based on the balanced realization [7] and that based on the impulse response Grammian [8] are not necessarily optimum in the sense of the L 2 norm in the approximation problem based on the 1D state-space model. They have proposed a method for designing an approximate filter with performance better than that of the conventional method by reducing the dimensions of the given FIR filter, using for this purpose an orthogonal projection in place of truncation of the coefficient matrix, and then optimizing the projection parameters.…”

Section: Introductionmentioning

confidence: 99%

Design of 2D separable‐denominator state‐space digital filters using orthogonal projection

Doi

Fujiwara

Hinamoto

2003

Electron Comm Jpn Pt III

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SUMMARYIn this paper, a design method is proposed for a two-dimensional separable-denominator state-space digital filter based on the projection method. First, the square error function is expressed in terms of the coefficient matrix of the local state-space model. Next, the given FIR filter is realized by a local state-space model. An equivalent transform based on the eigenvalue-eigenvector decomposition of the impulse response Grammian is applied to this filter. The obtained model is approximated at lower order by orthogonal projection. The projection parameters are optimized by an iterative algorithm based on the error function, deriving a lower dimensional model with a higher design accuracy. The conventional lower dimensional approximation algorithm based on rounding down of the coefficient matrix is used to find the initial values in the present method. The stability of the filter obtained by the present method is always guaranteed. The effectiveness of the present method is confirmed by numerical examples.

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Section: Introductionmentioning

confidence: 99%

Design of 2D separable‐denominator state‐space digital filters using orthogonal projection

Doi

Fujiwara

Hinamoto

2003

Electron Comm Jpn Pt III

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“…The solution is derived entirely in terms of the Markov parameters of the FIR filter which is approximated and can be expressed in either state-space or transfer-function form. Additional advantages of our method over parallel techniques [3], [5], [6], [12], [17] include computational efficiency and a unified treatment for the optimal and the sub-optimal case. The most recent reference in the area is [6] which develops an elegant self-contained approach for the solution of the optimal Hankel norm approximation problem of FIR filters in the scalar case.…”

Section: Introduction and Notationmentioning

confidence: 99%

Hankel-norm approximation of FIR filters: a descriptor-systems based approach

Halikias

Tsoulkas

Pantelous

et al. 2010

International Journal of Control

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We propose a new method for approximating a matrix Finite Impulse Response (FIR) filter by an Infinite Impulse Response (IIR) filter of lower McMillan degree. This is based on a technique for approximating discrete-time descriptor systems and requires only standard linear algebraic routines, while avoiding altogether the solution of two matrix Lyapunov equations which is computationally expensive. Both the optimal and the suboptimal cases are addressed using a unified treatment. A detailed solution is developed in state-space or polynomial form, using only the Markov parameters of the FIR filter which is approximated. The method is finally applied to the design of scalar Infinite Impulse Response (IIR) filters with specified magnitude frequency-response tolerances and approximately linear phase characteristics. A-priori bounds on the magnitude and phase errors are obtained which may be used to select the reduced-order IIR filter order which satisfies the specified design tolerances. The effectiveness of the method is illustrated with a numerical example. Additional applications of the method are also briefly discussed.

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“…The design of IIR filters with constant group delay in the passband is also carried out by using allpass structures through evaluation of phase response instead of approximating the group delay directly [29][30][31][32]. Some other methods used an indirect approach based on model reduction techniques where a linear-phase FIR filter that meets the required specifications is first designed and then a lower order IIR filter that meets the original amplitude specifications while maintaining a linear-phase response in the passband is obtained [33][34][35]. Coretlazzo et al [36] have achieved the simultaneous design in both magnitude and group delay of IIR and FIR filters based on multiple criterion optimizations.…”

Section: Introductionmentioning

confidence: 99%

Optimal Multiobjective Design of Digital Filters Using Taguchi Optimization Technique

Ouadi¹,

Bentarzi²,

Recioui³

2014

Journal of Electrical Engineering

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The multiobjective design of digital filters using the powerful Taguchi optimization technique is considered in this paper. This relatively new optimization tool has been recently introduced to the field of engineering and is based on orthogonal arrays. It is characterized by its robustness, immunity to local optima trapping, relative fast convergence and ease of implementation. The objectives of filter design include matching some desired frequency response while having minimum linear phase; hence, reducing the time response. The results demonstrate that the proposed problem solving approach blended with the use of the Taguchi optimization technique produced filters that fulfill the desired characteristics and are of practical use.

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Design of linear-phase IIR filters via impulse-response gramians

Cited by 53 publications

References 13 publications

Design of 2D separable‐denominator state‐space digital filters using orthogonal projection

Design of 2D separable‐denominator state‐space digital filters using orthogonal projection

Hankel-norm approximation of FIR filters: a descriptor-systems based approach

Optimal Multiobjective Design of Digital Filters Using Taguchi Optimization Technique

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