Two-dimensional Infinite Impulse Response Filters Research Articles

A Sequential Partial Optimization Algorithm for Minimax Design of Separable-Denominator 2-D IIR Filters

A sequential partial optimization method is presented in this paper for the minimax design of two-dimensional infinite impulse response filters with separable denominator. The method converts the minimax design problem into a sequence of smaller subproblems, each updating only one pair of second-order denominator factors. The necessary and sufficient stability triangles for one-dimensional filters are used as the stability constraints on the two-dimensional filters. The first-order Taylor expansion and a trust-region method are used to deal with the nonconvexity of the subproblems and guarantee the convergence of the solution algorithm. By comparing with a corresponding joint optimization method, the sequential partial optimization algorithm is shown to converge faster for filters with relatively high denominator order. This is mainly due to the observation that the trust region to assure the convergence is usually much smaller for the joint optimization method. Moreover, the limit solution of the sequential partial optimization algorithm has been proved to be a Karush–Kuhn–Tucker point of the design problem. Design examples demonstrate that the proposed algorithm has obtained smaller maximum frequency response errors than the competing methods both for filters with separable denominator of the same order and for filters with nonseparable denominator of about the same implementation complexity.

A swarm intelligence approach to the synthesis of two-dimensional IIR filters

The concept of particle swarms, although initially introduced for simulating human social behaviors, has become very popular these days as an efficient means for intelligent search and optimization. The particle swarm optimization (PSO), as it is called now, does not require any gradient information of the function to be optimized, uses only primitive mathematical operators and is conceptually very simple. This paper investigates a novel approach to the designing of two-dimensional zero phase infinite impulse response (IIR) digital filters using the PSO algorithm. The design task is reformulated as a constrained minimization problem and is solved by a modified PSO algorithm. Numerical results are presented. The paper also demonstrates the superiority of the proposed design method by comparing it with two recently published filter design methods and two other state of the art optimization techniques.

Design Two-Dimensional IIR Filters Based on Clonal Selection Algorithm with Singular Value Decomposition

In this letter, clonal selection algorithm (CSA) with singular value decomposition (SVD) method is investigated for the realization of two-dimentional (2D) infinite-impulse response (IIR) filters with arbitrary magnitude responses. The CSA is applied to optimize the sampled frequencies of transition band of digital filters, then producing a planar response matrix of a 2D IIR digital filter. By using the SVD, 2D magnitude specifications can be decomposed into a pair of 1D filters, and thus the problem of designing a 2D digital filter can be reduced to the one of designing a pair of 1D digital filters or even only one 1D digital filter. The stimulation results show the proposed method has the better performance of the minimum attenuation between the passband and stopband.

Design two-dimensional IIR filters based on clonal selection algorithm with singular value decomposition

In this letter, clonal selection algorithm (CSA) with singular value decomposition (SVD) method is investigated for the realization of two-dimentional (2D) infinite-impulse response (IIR) filters w...

TWO-DIMENSIONAL IIR FILTER DESIGN WITH MODERN SEARCH HEURISTICS: A COMPARATIVE STUDY

In the past few years, there has been a massive growth in the field of biologically inspired global search heuristics. Computational cost having been reduced almost dramatically, researchers from all corners are taking more interset in following the underlying principles of nature to solve nearly intractable search problems. In this paper, we attempt to solve one very important optimization problem arising in the field of two-dimensional IIR (infinite impulse response) filter design, with three naturally inspired global search algorithms. We have used a state-of-the-art real coded genetic algorithm (GA), one very recent and modified version of the particle swarm opimization (PSO) and finally an improved version of the differential evolution (DE) algorithm. The DE algorithm has been modified by us to prevent its premature convergence to some suboptimal region of the search space. The design task is formulated as a constrained minimization problem and solved by the three metaheuristics. Numerical results are presented over three difficult instances of the design problem. The study also compares the results with two recently published filter design methods. Our experiments reveal that the DE family of algorithms should receive primary attention in solving the constrained multidimensional filter design tasks.

Optimization-based design and implementation of multidimensional zero-phase IIR filters

This paper considers multidimensional infinite-impulse response (IIR) filters that are iteratively implemented. The focus is on zero-phase filters with symmetric polynomials in the numerator and denominator of the multivariable transfer function. A rigorous optimization-based design of the filter is considered. Transfer function magnitude specifications, convergence speed requirements for the iterative implementation, and spatial decay of the filter impulse response (which defines the boundary condition influence in the spatial domain of the filtered signal) are all formulated as optimization constraints. When the denominator of the zero-phase IIR filter is strictly positive, these frequency domain specifications can be cast as a linear program and then efficiently solved. The method is illustrated with two two-dimensional IIR filter design examples.

Optimization of two-dimensional IIR filters with nonseparable and separable denominator

We present algorithms for the optimization of two-dimensional (2-D) infinite impulse response (IIR) filters with separable or nonseparable denominator, for least squares or Chebyshev criteria. The algorithms are iterative, and each iteration consists of solving a semidefinite programming problem. For least squares designs, we adapt the Gauss-Newton idea, which outcomes to a convex approximation of the optimization criterion. For Chebyshev designs, we adapt the iterative reweighted least squares (IRLS) algorithm; in each iteration, a least squares Gauss-Newton step is performed, while the weights are changed as in the basic IRLS algorithm. The stability of the 2-D IIR filters is ensured by keeping the denominator inside convex stability domains, which are defined by linear matrix inequalities. For the 2-D (nonseparable) case, this is a new contribution, based on the parameterization of 2-D polynomials that are positive on the unit bicircle. In the experimental section, 2-D IIR filters with separable and nonseparable denominators are designed and compared. We show that each type may be better than the other, depending on the design specification. We also give an example of filter that is clearly better than a recent very good design.

Design of Stable IIR Digital Filter Based on Least<tex>$rm P$</tex>-Power Error Criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.

The application of two-dimensional finite-precision IIR filters to enhanced NTSC coding

The goal of this paper is to study the application of two-dimensional (2-D) finite-precision infinite impulse response (IIR) filters to enhanced National Television System Committee (NTSC) coding. It is well-known that suitable twoor three-dimensional (3-D) digital filtering greatly improves the quality of NTSC pictures by suppressing the interference between the luminance Y and the chrominances I, Q. Thus far, 2-D and 3-D finite impulse response (FIR) filters have been used to reduce or eliminate these cross effects. To achieve good performance, however, they require many coefficients. Since, in general, IIR filters need fewer coefficients to approximate a given magnitude response, we investigate the possibility of applying 2-D IIR filters to the NTSC encoding/decoding. We also study the feasibility of using digital filters for NTSC channel filtering; this would permit a digital-only encoder. To design suitable filters, we use a method based on multiple constraint optimization and simulated annealing. We propose a new implementation structure for the IIR filters that differs from the zero-phase FIR structure. We simulate the full NTSC coding chain and compare the resulting images for both filter types.

Design of two-dimensional circularly symmetric low-pass IIR filters using transformation

A technique for designing two-dimensional IIR (infinite-impulse response) filters using a separable transformation function has been reported recently. A modification of this technique is proposed for circularly symmetric filters which gives better results. >