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Journal ArticleDOI

Design of discrete-coefficient FIR filters on loosely connected parallel machines

01 Jun 2002-IEEE Transactions on Signal Processing (IEEE)-Vol. 50, Iss: 6, pp 1409-1416

TL;DR: A new branch-and-bound mixed-integer linear programming-based algorithm for designing discrete-coefficient finite-impulse response (FIR) filters using a cluster of workstations as the computation platform and test run results showed that super linear speedup may be achieved.

AbstractThis paper presents a new branch-and-bound mixed-integer linear programming-based algorithm for designing discrete-coefficient finite-impulse response (FIR) filters using a cluster of workstations as the computation platform. The discrete coefficient space considered is the sum of signed power-of-two space, but the technique is also applicable to other discrete coefficient spaces. The key issue determining the success of the algorithm is the ability to partition the original problem into several independent parts that can be distributed to a cluster of machines for solution. The master-slave model is adopted for the control of the machines. Test run results showed that super linear speedup (i.e., the speedup factor is more than the number of machines running in parallel) may be achieved.

Topics: Speedup (59%), Branch and bound (54%), Linear programming (53%), Integer programming (51%), Signal processing (50%)

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Citations
More filters

Journal Article
TL;DR: A new method for allocating the number of SPT terms to each coefficient value is presented, determined by the statistical quantization step-size of that coefficient and the sensitivity of the frequency response of the filter to that coefficient.
Abstract: It is well known that if each coefficient value of a digital filter is a sum of signed power-of-two (SPT) terms, the filter can be implemented without using multipliers. In the past decade, several methods have been developed for the design of filters whose coefficient values are sums of SPT terms. Most of these methods are for the design of filters where all the coefficient values have the same number of SPT terms. It has also been demonstrated recently that significant advantage can be achieved if the coefficient values are allocated with different number of SPT terms while keeping the total number of SPT terms for the filter fixed. In this paper, we present a new method for allocating the number of SPT terms to each coefficient value. In our method, the number of SPT terms allocated to a coefficient is determined by the statistical quantization step-size of that coefficient and the sensitivity of the frequency response of the filter to that coefficient. After the assignment of the SPT terms, an integer-programming algorithm is used to optimize the coefficient values. Our technique yields excellent results but does not guarantee optimum assignment of SPT terms. Nevertheless, for any particular assignment of SPT terms, the result obtained is optimum with respect to that assignment.

163 citations


Journal ArticleDOI
TL;DR: A novel optimization technique is proposed to optimize filter coefficients of linear phase finite-impulse response (FIR) filter to share common subexpressions within and among coefficients by optimizing the filter coefficients directly in subexpression space for a given specification.
Abstract: In this paper, a novel optimization technique is proposed to optimize filter coefficients of linear phase finite-impulse response (FIR) filter to share common subexpressions within and among coefficients. Existing approaches of common subexpression elimination optimize digital filters in two stages: first, an FIR filter is designed in a discrete space such as finite wordlength space or signed power-of-two (SPT) space to meet a given specification; in the second stage, an optimization algorithm is applied on the discrete coefficients to find and eliminate the common subexpressions. Such a two-stage optimization technique suffers from the problem that the search space in the second stage is limited by the finite wordlength or SPT coefficients obtained in the first stage optimization. The new proposed algorithm overcomes this problem by optimizing the filter coefficients directly in subexpression space for a given specification. Numerical examples of benchmark filters show that the required number of adders obtained using the proposed algorithm is much less than those obtained using two-stage optimization approaches.

92 citations


Cites methods from "Design of discrete-coefficient FIR ..."

  • ...First we review the depth-first search branch and bound algorithm [21]–[23] which has successfully optimized filter coeffi-...

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Journal ArticleDOI
TL;DR: This paper presents a method to implement FIR filters for SDR receivers using minimum number of adders, using an arithmetic scheme, known as pseudo floating-point (PFP) representation to encode the filter coefficients.
Abstract: The most computationally intensive part of the wideband receiver of a software defined radio (SDR) is the intermediate frequency (IF) processing block. Digital filtering is the main task in IF processing. The computational complexity of finite impulse response (FIR) filters used in the IF processing block is dominated by the number of adders (subtracters) employed in the multipliers. This paper presents a method to implement FIR filters for SDR receivers using minimum number of adders. We use an arithmetic scheme, known as pseudo floating-point (PFP) representation to encode the filter coefficients. By employing a span reduction technique, we show that the filter coefficients can be coded using considerably fewer bits than conventional 24-bit and 16-bit fixed-point filters. Simulation results show that the magnitude responses of the filters coded in PFP meet the attenuation requirements of wireless communication standard specifications. The proposed method offers average reductions of 40% in the number of adders and 80% in the number of full adders needed for the coefficient multipliers over conventional FIR filter implementation methods

56 citations


Cites background from "Design of discrete-coefficient FIR ..."

  • ...All previous work on filter implementation [5]-[9] discussed hardware reduction in terms of the number of adders and has not addressed the complexity of adders....

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  • ...The number of adders needed in the multipliers is proportional to the coefficient wordlength [9]....

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BookDOI
01 Jan 2013
TL;DR: This book focuses on and around new implementation techniques of discrete wavelet transform (DWT) and their applications in denoising and classification and their impact on signal processing theory and practice.
Abstract: Wavelet transforms (WT) have growing impact on signal processing theory and practice. This is because of two reasons: (a) unifying role of wavelet transform and (b) their successes in wide variety of applications. Digital filter banks, the basis of wavelet-based algorithms, have become standard signal processing operators. Filter banks are the fundamental tools required for processing of real signals using digital signal processors (DSP) [133,139]. Vaidyanathan in his book [134] has discussed connection between theory of filter bank and DSP. The purpose of this book is to look at wavelet-related issues from a signal processing perspective. This book focuses on and around new implementation techniques of discrete wavelet transform (DWT) and their applications in denoising and classification. On this account, it is required to introduce the wavelet theory in brief. The organization of this chapter is as follows: Section 1.1 introduces the subject in brief. Section 1.2 presents historical review of multiresolution analysis and wavelet transform. Various kinds of wavelet transform applied to signal processing applications viz. continuous wavelet transform (CWT) and DWT (one dimension and two dimensions) are discussed in brief. Section 1.3 reviews implementation issues and applications of DWT from signal processing viewpoint. Section 1.4 concludes this chapter by outlining major contribution of the book.

34 citations


Journal ArticleDOI
TL;DR: In this work, a novel genetic algorithm (GA) is proposed for the design of multiplierless linear phase finite impulse response (FIR) filters, and significantly outperforms existing algorithms dealing with the similar problems in terms of design time and hardware cost.
Abstract: In this work, a novel genetic algorithm (GA) is proposed for the design of multiplierless linear phase finite impulse response (FIR) filters. The filters under consideration are of high order and wide coefficient wordlength. Both the single-stage and cascade form are considered. In a practical filter design problem, when the filter specification is stringent, requiring high filter order and wide coefficient wordlength, GAs often fail to find feasible solutions, because the discrete search space thus constructed is huge and the majority of the solution candidates therein can not meet the specification. In the proposed GA, the discrete search space is partitioned into smaller ones. Each small space is constructed surrounding a base discrete coefficient set which is obtained by a proposed greedy algorithm. The partition of the search space increases the chances for the GA to find feasible solutions, but does not sacrifice the coverage of the search. The proposed GA applies to the design of single-stage filters. When a cascade form filter is designed, for each single-stage filter meeting the filter specification generated during the course of GA, an integer polynomial factorization is applied. Design examples show that the proposed GA significantly outperforms existing algorithms dealing with the similar problems in terms of design time, and the hardware cost is saved in most cases.

28 citations


References
More filters

Book
01 Jan 1972
Abstract: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization. This highly respected and much-cited text, a standard of graduate-level courses since 1972, presents a comprehensive treatment of the first two decades of research on integer programming.

4,157 citations


"Design of discrete-coefficient FIR ..." refers background in this paper

  • ...The penalty value [28] of a constraint is the degradation on the objective function when the constraint is imposed....

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Journal ArticleDOI
TL;DR: If the frequency responses of the original ( M + 1) -band filter and its complementary filter are properly masked and recombined, narrow transition-band filter can be obtained and this technique can be used to design sharp low-pass, high- pass, bandpass, and bandstop filters with arbitrary passband bandwidth.
Abstract: If each delay element of a linear phase low-pass digital filter is replaced by M delay elements, an (M + 1) -band filter is produced. The transition-width of this (M + 1) -band filter is 1/M that of the prototype low-pass filter. A complementary filter can be obtained by subtracting the output of the (M + 1) -band filter from a suitably delayed version of the input. The complementary filter is an (M + 1) -band filter whose passbands and stopbands are the stopbands and passbands, respectively, of the original (M + 1) -band filter. If the frequency responses of the original ( M + 1) -band filter and its complementary filter are properly masked and recombined, narrow transition-band filter can be obtained. This technique can be used to design sharp low-pass, high-pass, bandpass, and bandstop filters with arbitrary passband bandwidth.

470 citations


"Design of discrete-coefficient FIR ..." refers background in this paper

  • ...Many papers on finite wordlength or power-of-two design technique [1]–[7], [13]–[21] and sparse coefficient techniques [22]–[26] have been published in the literature....

    [...]


Journal ArticleDOI
Abstract: FIR digital filters with discrete coefficient values selected from the powers-of-two coefficient space are designed using the methods of integer programming. The frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients. Both the weighted minimax and the weighted least square error criteria are considered. Using a weighted least square error criterion, it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding.

443 citations


Journal ArticleDOI
Abstract: An efficient method optimizing (in the least square response error sense) the remaining unquantized coefficients of a FIR linear phase digital filter when one or more of the filter coefficients takes on discrete values is introduced. By incorporating this optimization method into a tree search algorithm and employing a suitable branching policy, an efficient algorithm for the design of high-order discrete coefficient FIR filters is produced. This approach can also be used to design FIR filters on a minimax basis. The minimax criterion is approximated by adjusting the least squares weighting. Results show that the least square criteria is capable of designing filters of order well beyond other approaches by a factor of three for the same computer time. The discrete coefficient spaces discussed include the evenly distributed finite wordlength space as well as the nonuniformly distributed powers-of-two space.

240 citations


"Design of discrete-coefficient FIR ..." refers methods in this paper

  • ...It should be noted that the computer time required by running MILP is several orders of magnitude [29] of that required by other suboptimum techniques if only one processor is used; running MILP on parallel machines still requires more computer time than running other techniques on a single…...

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  • ...Mixed-integer linear programming (MILP) is the only known method that can provide the global optimum solution to the design of FIR filters with SPT coefficient values [2], [4], [27], although other computationally very much less demanding technique exist [29]....

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Journal ArticleDOI
TL;DR: Universal randomized methods for parallelizing sequential backtrack search and branch-and-bound computation are presented and demonstrate the effectiveness of randomization in distributed parallel computation.
Abstract: Universal randomized methods for parallelizing sequential backtrack search and branch-and-bound computation are presented. These methods execute on message-passing multi- processor systems, and require no global data structures or complex communication protocols. For backtrack search, it is shown that, uniformly on all instances, the method described in this paper is likely to yield a speed-up within a small constant factor from optimal, when all solutions to the problem instance are required. For branch-and-bound computation, it is shown that, uniformly on all instances, the execution time of this method is unlikely to exceed a certain inherent lower bound by more than a constant factor. These randomized methods demonstrate the effectiveness of randomization in distributed parallel computation. Categories and Subject Descriptors: F.2.2 (Analysis of Algorithms and Problem Complexity): Non-numerical Algorithms-computation

187 citations