Design of hardware efficient FIR filter: A review of the state-of-the-art approaches

Most wavelet filters reported in the literature have irrational coefficients. Hardware implementation can be simpler if the filter coefficients are rational valued. In this paper, we present novel methods to rationalize both orthogonal and biorthogonal filter coefficients with perfect reconstruction and vanishing moments preservation. Rational orthogonal filter coefficients are obtained using lattice structures. Rational biorthogonal filter coefficients are obtained using the complementary filter technique in which one set of filter coefficients is expressed in terms of the other. The rationalized filters have characteristics that are very close to the original irrational filters. The techniques are simple yet general enough to be used for almost any filter bank unlike the techniques in previously reported works.

New Techniques for Rationalizing Orthogonal and Biorthogonal Wavelet Filter Coefficients

Recently, the design of the two-dimensional digital filter has become a subject of interest in the field of two-dimensional signal processing. The two-dimensional digital filter has been applied in many important areas such as image processing, television systems and seismic signal processing. In digital filter design, there are several indispensable aims such as stability, reduced computational complexity and computational time. Thus, researchers and practitioners have investigated various advanced methods based on metaheuristic optimization algorithms for the design of the two-dimensional digital filter. Metaheuristic optimization algorithms have been applied to solve different complicated problems in various fields and they have also been successfully used in digital filter design. This paper presents a review of the design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms such as the genetic algorithm, differential evolution and particle swarm optimization. By comparing the proposed design approaches based on metaheuristic optimization algorithms, it is observed that the genetic algorithm is the most preferred algorithm and emerging novel algorithms using metaheuristic optimization algorithms have better performance in terms of computational complexity and computational time. It is hoped that this review will be helpful for researchers and practitioners studying the design of two-dimensional digital filters.

The design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms: a review of the literature

Design of efficient circularly symmetric two-dimensional variable digital FIR filters

In this paper, we present a novel and efficient method for the design of a sharp, two dimensional (2D) wideband, circularly symmetric, FIR filter. First of all, a sharp one dimensional (1D) infinite precision FIR filter is designed using the Frequency Response Masking (FRM) technique. This filter is converted into a multiplier-less filter by representing it in the Canonic Signed Digit (CSD) space. The design of the FRM filter in the CSD space calls for the use of a discrete optimization technique. To this end, a new optimization approach is proposed using a modified Harmony Search Algorithm (HSA). HSA is modified in such a way that, in every exploitation and exploration phase, the candidate solutions turns out to be integers. The 1D FRM multiplier-less filter, is in turn transformed to the 2D equivalent using the recently proposed multiplier-less transformations namely, T1 and T2. These transformations are successful in generating circular contours even for wideband filters. Since multipliers are the most power consuming elements in a 2D filter, the multiplier-less realization calls for reduced power consumption as well as computation time. Significant reduction in the computational complexity and computation time are the highlights of our proposed design technique. Besides, the proposed discrete optimization using modified HSA can be used to solve optimization problems in other engineering disciplines, where the search space consists of integers.

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Design of Sharp 2D Multiplier-Less Circularly Symmetric FIR Filter Using Harmony Search Algorithm and Frequency Transformation

In this paper, we modify the original McClellan transformation to a th-order version, and on the basis of the th-order McClellan transformation, we propose two high-order transformations for designing circularly symmetric wideband two-dimensional (2-D) digital FIR filter. The circularity of the resulting 2-D filters designed by our transformations is comparable to those 2-D filters designed by the other methods; however, the existing methods for circularly symmetric design cannot obtain a 2-D filter by the application of a single transformation on the 1-D filter response. By using the proposed transformations, in a single transformation on the 1-D filter, we can easily obtain the circularly symmetric 2-D digital FIR filter over a wide range of cutoff frequencies. Besides, with our approach, neither optimization procedure nor any computation is needed to obtain the transformation. Furthermore, since the implementations of the transformations are all multiplierless, the resulting 2-D filter has the same number of multipliers with the 1-D prototype filter. In the narrowband case, the 2-D transition width is shown to be narrower by a factor of about (and ) than the transition width of the 1-D prototype filter. This means that the filter length required in the prototype filter is shorter than that using the existing methods.

Design of 2-D Wideband Circularly Symmetric FIR Filters by Multiplierless High-Order Transformation

In this article, a transformation (subfilter) for designing finite impulse response (FIR) Hilbert transformers (HTs) is proposed. With our approach, except simple search procedures, neither optimisation nor any filter design algorithm is needed to obtain the transformation. The proposed subfilter requires only two multipliers regardless of the subfilter order. For the frequency transformation design, the purpose of the subfilter is to provide a “rough” shape of the desired HT; the two coefficients of the subfilter can be implemented as the form of sum of power of two (SOPOT) with only a few bits, thus leading to a multiplierless realisation. Moreover, by applying the transformation on the subfilter again, a technique named as nested frequency transformation (nested FT) is introduced. This technique can further reduce the number of multipliers needed in the overall HT.

Yang-Lung Tai

Papers

Design of 2-D Wideband Circularly Symmetric FIR Filters by Multiplierless High-Order Transformation

Design of FIR Hilbert transformers using prescribed subfilters and nested FT technique