Design of discrete-coefficient FIR filters on loosely connected parallel machines
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.
Abstract: This 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.
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
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.
96 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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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
59 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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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.
36 citations
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.
33 citations
References
More filters
TL;DR: In this paper, an expression for the impulse response up-sampling ratio M, which will produce a minimum complexity design, is derived, and an optimum design relationship for the interpolated impulse response technique is also derived.
Abstract: An expression for the impulse response up-sampling ratio M, which will produce a minimum complexity design, is derived. It is shown that M approaches e (the base of the natural logarithm) as the number of frequency response masking stages increases; in a K-stage design the complexity of the filter is inversely proportional to the (K+1)th root of the transition width; the frequency response masking technique is effective if the normalized transition width is less than 1/16; and the frequency response masking technique is more efficient than the interpolated impulse response technique if the square root of the normalized transition width is less than the arithmetic mean of the normalized passband edge and stopband edge. An expression for the multistage frequency response ripple compensation is derived. An optimum design relationship for the interpolated impulse response technique is also derived. The design of narrow-band two-dimensional filters using the frequency response masking technique is also presented. >
183 citations
TL;DR: Four methods are presented for optimizing filters in the normalized peak ripple magnitude (NPRM) sense, two of the methods being to the passband gain sectioning technique and several heuristic methods for determining alpha.
Abstract: Four methods are presented for optimizing filters in the normalized peak ripple magnitude (NPRM) sense. Two of the methods being to the passband gain sectioning technique. The other two methods make use of the objective function f= delta - alpha b. Several heuristic methods for determining alpha are also presented. The NPRM is an important performance measure; the absolute peak ripple magnitude and passband gain are less important. In these applications, the passband gain need not be fixed at unity but should be a continuous variable to the optimized. Nevertheless, an upper and a lower bound on the passband gain should be imposed to satisfy overflow and roundoff noise performance requirements. >
166 citations
TL;DR: The application of a general-purpose integer-programming computer program to the design of optimal finite wordlength FIR digital filters is described and an analysis of the approach based on the results of more than 50 design cases is presented.
Abstract: The application of a general-purpose integer-programming computer program to the design of optimal finite wordlength FIR digital filters is described. Examples of two optimal low-pass FIR finite wordlength filters are given and the results are compared with the results obtained by rounding the infinite wordlength coefficients. An analysis of the approach based on the results of more than 50 design cases is presented and the problem of optimal wordlength choice is discussed.
164 citations
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
"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....
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TL;DR: In this article, 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.
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.
145 citations