Design Of FIR Digital Filters Research Articles

Design of optimal linear phase FIR high pass filter using craziness based particle swarm optimization technique

In this paper, an optimal design of linear phase digital high pass FIR filter using Craziness based Particle Swarm Optimization (CRPSO) approach has been presented. FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for such multi-modal optimization problem as they are susceptible to getting trapped on local optima. Given the desired filter specifications to be realized, the CRPSO algorithm generates a set of optimal filter coefficients and tries to meet the desired specifications. In birds’ flocking or fish schooling, a bird or a fish often changes directions suddenly. This is described by using a ‘‘craziness’’ factor and is modeled in the CRPSO technique. In this paper, the realizations of the CRPSO based optimal FIR high pass filters of different orders have been performed. The simulation results have been compared to those obtained by the well accepted classical optimization algorithm such as Parks and McClellan algorithm (PM), and evolutionary algorithms like Real Coded Genetic Algorithm (RGA), and conventional Particle Swarm Optimization (PSO). The results justify that the proposed optimal filter design approach using CRPSO outperforms PM, RGA and PSO, in the optimal characteristics of frequency spectrums.

Optimization of Control Parameters of Differential Evolution Technique for the Design of FIR Pulse-shaping Filter in QPSK Modulated System

Signal Processing in modern era, involves rigorous applications of various evolutionary algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE) for the optimized design of aerodynamic shape, automated mirror, digital filter, computational intelligence etc. DE has been judged to be quite effective in designing different types of digital filter with good convergence behavior. The performance of the DE optimization technique could be improved to a further extent if the values of the two control parameters namely “Weighting Factor” and “Crossover Probability”, be chosen properly. In this paper, the effect of these two control parameters on the design of low pass FIR digital filter has extensively been studied. The impact of these control parameters on the convergence behavior of the DE technique has also been presented. The performance of the DE optimized filter has been adjudicated in terms of its magnitude and impulse responses. In addition, the DE optimized filter has been utilized as a pulse-shaping filter in a Quadrature Phase Shift Keying (QPSK) modulated system and its performance has further been studied in terms of Bit Error Rate (BER). Finally, the optimized values of the ‘’Weighting Factor’’ and “Crossover Probability” for this specific modulated system design problem has been recommended. Experimentally measured Eye diagrams have also confirmed the optimized values.

Design of Optimal Comb FIR Filters-Speed and Robustness

An extension to the analytical design of digital equiripple comb FIR filters is presented here. The filters are optimal in Chebyshev sense. The design runs from the filter specification through the degree formula to the impulse response coefficients, which are evaluated by an extremely efficient recursive algorithm. The proposed design method outperforms the standard procedures in terms of speed and robustness.

Sinc Sum Function and Its Application on FIR Filter Design

A new function is found and is defined as sinc sum function by the author. It has outstanding properties of stairs shape, global symmetry, local symmetry, derivative formula simplicity, local extreme certainty, oscillation regularity, extreme value stability, etc. These properties are proved. Geometry meaning is explained. As an application of the function, the author has developed a new method to design FIR digital filters with adjustable weights. Filter formula in time domain is the weighted sum of sub-filters. A novel form of frequency response expression is deduced which is the sum of sinc sum functions. One of the remarkable characteristics of the form is that weights of sub-filters can be directly calculated according to the expression. Completing the calculation of the weights means finishing the design of a filter. The weights can be either adjustable or fixed. A method to determine the weights are given. Three examples using the method are selected for the consideration that the new method can be easily compared with some famous window methods. Three new filter formulas are produced. Much better performances can be obtained using these formulas compared with using Hanning window and Blackman window respectively. And the performance designing with the new method is slightly better than that with Hamming window. For fixed weights it is almost as easy as using fixed window to calculate filter coefficients.

Design of Variable Two-Dimensional FIR Digital Filters by McClellan Transformation

In this paper, the technique of McClellan transformation is applied to design variable 2-D FIR digital filters. Compared with the conventional transformation, the 2-D transformation subfilter and the 1-D prototype filter are designed such that their frequency characteristics are adjustable. Moreover, they are tunable by the same variable parameter, so the variable characteristics of 1-D prototype filters are coincident with those of 2-D subfilters. Several examples, including variable fan filters, variable circularly symmetric filters, and variable elliptically symmetric filters with arbitrary orientation, are presented to demonstrate the effectiveness and the flexibility of the presented method.

A generalized approach to the design of variable fractional-delay FIR digital filters

In this paper, a complex-oriented weighted least-squares approach is proposed for the design of arbitrary variable fractional-delay FIR filters. The objective error function is formulated in a quadratic form, such that the filter coefficients can be obtained by proper matrix/vector operation, including matrix inversion. However, all elements of related matrices and vectors can be represented in closed forms, and the matrix to be inversed is a positive-definite Hermitian symmetric matrix, which can be decomposed by the Cholesky factorization, such that computation time can be effectively reduced and the ill condition can be avoided. Comparing with the existing methods, the proposed method can be applied to design arbitrary complex coefficient or real coefficient variable fractional-delay filters. Several examples are presented to demonstrate the flexibility and effectiveness of the proposed method.

Design of 2D FIR and IIR Digital Filters with Canonical Signed Digit Coefficients Using Singular Value Decomposition and Genetic Algorithms

In this paper a design approach for two-dimensional finite impulse and infinite impulse response digital filters with canonic signed digit (CSD) coefficients based on singular value decomposition and genetic algorithms (GAs) is presented. The proposed technique uses a new chromosome coding scheme to alleviate the problem encountered by many GAs during crossover and mutation which destroys the CSD property. Examples are given to demonstrate the usefulness of the proposed technique. A comparative study carried out with some of the existing techniques indicates the high throughput property of the proposed technique.

Optimization of FRM FIR Digital Filters Over CSD and CDBNS Multiplier Coefficient Spaces Employing a Novel Genetic Algorithm

It is well known that frequency response masking (FRM) FIR digital filters can be designed to exhibit very sharp-transition bands at the cost of slightly larger filter lengths as compared to the conventional FIR digital filters. The FRM FIR digital filters permit efficient hardware implementations due to an inherently large number of zerovalued multiplier coefficients in their transfer functions. The hardware complexity of these FIR digital filters can be further reduced by employing computationally efficient number systems for the representation of the constituent non-zero-valued multiplier coefficients. This paper presents a novel genetic algorithm for the design and discrete optimization of FRM FIR digital filters over the conventional canonical signed-digit (CSD) as well as the emerging double base number system (DBNS) multiplier coefficient spaces. This genetic algorithm is based on a pair of indexed look-up tables (LUTs) of permissible CSD/DBNS numbers whose indices form a closed set under the genetic algorithm operations of crossover and mutation. The CSD/DBNS values themselves permit pre-specified word-lengths and pre-specified number of non-zero bits. The salient feature of the proposed genetic algorithm is that it automatically leads to legitimate CSD/DBNS multiplier coefficients without any recourse to gene repair during optimization. The main features of the proposed genetic algorithm are demonstrated through its application to the design of a pair of low-pass and band-pass FRM FIR digital filters.

Design of narrowband frequency sampling FIR filters using Z-window

In this work a method for automatic design of narrowband frequency sampling low-pass digital FIR filters is presented. Spectral response of Zhong (Z)-window has been used to provide the filtering action. Z-windows are used as variable windows by varying the side-lobe dip position. The proposed design methodology is a hybridization of the concepts of frequency sampling method and window method of filter design. This proposed design technique produces low-pass FIR filters featuring sharp cut off, exactly marked pass-band and cut off frequencies along with tolerable pass-band ripple and variable stop-band attenuation. For the filter applications requiring brick-wall response, considerable saving in the filter order can be achieved with subsequent reduction in computational and storage requirements by this method.

Design of narrowband frequency sampling FIR filters using Z-window

In this work a method for automatic design of narrowband frequency sampling low-pass digital FIR filters is presented. Spectral response of Zhong (Z)-window has been used to provide the filtering action. Z-windows are used as variable windows by varying the side-lobe dip position. The proposed design methodology is a hybridization of the concepts of frequency sampling method and window method of filter design. This proposed design technique produces low-pass FIR filters featuring sharp cut off, exactly marked pass-band and cut off frequencies along with tolerable pass-band ripple and variable stop-band attenuation. For the filter applications requiring “brick–wall” response, considerable saving in the filter order can be achieved with subsequent reduction in computational and storage requirements by this method.

Design method of FIR filters with the variable piecewise stopband

AbstractIn the field of digital signal processing, there are cases in which the frequency characteristics must be changed instantaneously in response to the processing objective. A filter whose characteristic can be varied instantaneously is called a variable filter. Many reports are available on the design of FIR digital filters with a variable passband. However, it appears that there are no publications on the design of an FIR digital filter in which the portion of the stopband with high attenuation can be varied. In this paper, a design method is proposed for an FIR digital filter using spectral parameters that make the portion of the stopband with high attenuation variable. For the design, the successive projection method with a simple algorithm is applied. A filter with an almost equal‐ripple profile for the entire amplitude characteristic is designed by varying the spectral parameters. As a result, it is possible to obtain amplitude characteristics close to those of the filter solved by the Remez algorithm for specifications that change instantaneously from time to time. Finally, a design example is presented to confirm the effectiveness of the present approach. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(4): 34–41, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20176

An efficient closed-form approach to the design of linear-phase FIR digital filters with variable-bandwidth characteristics

This paper deals with the design of variable-bandwidth linear-phase FIR digital filters. Such filters are implemented as a linear combination of fixed-coefficient linear-phase filters and the variable bandwidth characteristics are provided by a tuning parameter embedded in the filter structure. These filters are designed in a least-square sense by formulating an error function reflecting the difference between the desired variable bandwidth filter and the practical filter represented as a linear combination of fixed-coefficient filters in a quadratic form. The filter coefficients are obtained by solving a system of linear equations comprising of a block-symmetric positive-definite matrix in which each block is a Toeplitz-plus-Hankel matrix. Consequently, a significant reduction in computational complexity can be achieved in obtaining the entries of this matrix. Moreover, closed-form expressions are provided for both the block-symmetric matrix as well as the vector involved in the system of linear equations.

A weighted [formula omitted]-based method for the design of arbitrary one-dimensional FIR digital filters

In FIR filter design problems, filter specifications do not constrain in any way the ideal frequency response inside the transition regions. Most existing L2-based filter design techniques utilize this flexibility in order to improve their performance. In this paper we propose a new general method for the weighted L2-based design of arbitrary FIR filters. In particular, we propose a well-defined optimization criterion that depends on the selection of the desired response inside the transition regions. By optimizing our criterion we obtain desired responses that produce weighted mean square error optimum filters with extremely good characteristics. The proposed method is computationally simple since it requires the solution of a linear system of equations.

Design of complex-valued variable FIR digital filters and its application to the realization of arbitrary sampling rate conversion for complex signals

This brief studies the design of complex-valued variable digital filters (CVDFs) and their applications to the efficient arbitrary sample rate conversion for complex signals. The design of CVDFs using either the minimax or least-squares criteria is formulated as a convex optimization problem and solved using the second-order cone programming (SOCP). In addition, linear and convex quadratic inequality constraints can be readily incorporated. Design examples are given to demonstrate the effectiveness of the proposed approach.

New algorithm for fir filter design with discrete coefficients

This paper develops a new algorithm based on the Projected Gradient Algorithm (PGA) for the design of FIR digital filters with “sum of power of two” coefficients. It is shown that the integer programming involved in the FIR filter design can be solved by this algorithm. It is compared with the reported method for a SemiDefinite Programming (SDP) relaxation-based design. The simulations demonstrate that the new algorithm often yields the similar error performances of the FIR filter design, but the average CPU time of this approach is significantly reduced.

Telescoping rounding for suboptimal finite wordlength FIR digital filter design

Rounding of the so-called infinite precision coefficients to their nearest finite wordlength representation is often used for reasons of simplicity. This rounding, however, is typically far from optimal. A significantly better rounding method that uses a technique called telescoping is presented in this paper. Its practical effectiveness in the design of suboptimal finite wordlength filters is demonstrated. It can also be used to speed up the algorithms for optimal finite wordlength FIR filter design.

A Weighted Least-Square-Based Approach to FIR Filter Design Using the Frequency-Response Masking Technique

This paper presents a new method for the design of sharp linear phase FIR filters using the frequency-response masking (FRM) technique. The method is based on a weighted least square (WLS) approach, and the design problem is solved iteratively. The original least square (LS) problem is decomposed into two LS problems, each of which can be solved analytically. The effectiveness of the method is demonstrated through the design of a lowpass linear phase sharp FIR digital filter.

Digital pulse-shaping FIR filter design with reduced intersymbol and interchannel interference

Digital pulse-shaping FIR filter design with reduced intersymbol and interchannel interference

Digital pulse-shaping FIR filter design with reduced intersymbol and interchannel interference

An important requirement in the design of data transmission filters is the minimization of intersymbol interference, which is zero if the overall impulse response (transmit filter, channel and receive filter) satisfies the first Nyquist criterion. In this context, an important class of transfer functions, satisfying the Nyquist criterion, is the raised-cosine filter family. In order to guarantee low interference between adjacent channels, the transmit and receive filters must have a high value of stopband attenuation, so as to reduce the interchannel interference as much as possible. In this paper, a design method for finding the coefficients of a pair of linear-phase transmit/receive FIR filters, that when cascaded have raised-cosine frequency response, is presented. The design is based on Frequency Sampling techniques, and the filter parameters are chosen in order to obtain maximum stopband attenuation and low intersymbol interference. The filter coefficients can be easily evaluated and the optimal filter parameters can be obtained with tables or equations. The design method is very simple, completely automatic and suited for non-filter-oriented users. Look-up table techniques can be used for automatic re-design of the transmit and receive filters, making the proposed solution well suited to programmable computing platforms (FPGA—Field Programmable Gate Arrays- and PLD---Programmable Logic Devices-based platforms), or for applications where the design must be performed without any user intervention. The proposed filter design technique is quite simple and the results obtained often match the performance of filter designed using computationally more complex and conceptually more difficult methods. Copyright © 2003 AEI.

Designing linear phase FIR digital filters with flat passband and equiripple stopband characteristics

AbstractIt is known that linear phase FIR digital filters fall into four types considering the symmetry of impulse response. For example, filters of type 2 can be used at the time of partitioning and reconstruction of signals in multirate signal processing, and other types have similar special applications. Moreover, the linear phase FIR digital filters with flat passband and equiripple stopband characteristics are very important filters in practice because they have better time domain characteristics and less ringing than Chebyshev filters with equiripple stopband and passband characteristics. However, conventional design methods are restricted to type 1. In this paper, we therefore propose a method of design of linear phase FIR digital filters with flat passband and equiripple stopband characteristics for all four types. The proposed function is composed of two functions, one with a flat characteristic in the passband and the second with equiripple characteristics in the stopband. The latter function is obtained by using the well‐known Remez algorithm only for the stopband. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(4): 89–95, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1148