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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.
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.

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Citations
More filters
Journal ArticleDOI
TL;DR: A theorem that gives the lower bound on the increase in minimax approximation error that is caused by the finite wordlength restriction is presented and its extension and application to filter design cases is demonstrated.
Abstract: In many practical situations, it is necessary to represent the coefficients of a finite impulse response (FIR) digital filter by a finite number of bits. This not only degrades the filter frequency response but also introduces a theoretical limit on the performance of the filter. Derivation of a lower bound on filter degradation is the purpose of this paper. We consider a general case of a length N filter with a discrete set of allowable coefficients. A theorem that gives the lower bound on the increase in minimax approximation error that is caused by the finite wordlength restriction is presented. Its extension and application to filter design cases is demonstrated. The importance of this bound is not only theoretical. Its practical effectiveness is shown in the algorithm for optimal finite wordlength FIR filter design where it significantly reduces the amount of computation.

25 citations


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

  • ...The total computing time reduction factor was 2.1....

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Journal ArticleDOI
TL;DR: An extrapolated impulse response filter with residual compensation is proposed for the design of discrete coefficient finite-impulse response (FIR) filters using subexpression sharing and the reduced degree of freedom of filter coefficients due to the quasi-periodic approximation is perfectly restored.
Abstract: In this paper, an extrapolated impulse response filter with residual compensation is proposed for the design of discrete coefficient finite-impulse response (FIR) filters using subexpression sharing. The proposed technique utilizes the quasi-periodic nature of the filter impulse response to approximate the filter coefficients. The reduced degree of freedom of filter coefficients due to the quasi-periodic approximation is perfectly restored by introducing a residual compensation technique. The resulting subexpression sharing synthesis of discrete coefficient FIR filters has lower complexities than that of the conventional synthesis techniques in terms of number of adders. To further reduce the synthesis complexity, filter coefficients and residuals may be optimized in subexpression spaces. Mixed integer linear programming is formulated for the optimization. Numerical examples show that the number of adders required by synthesizing the filters in the proposed structure is significantly reduced compared to that of the conventional synthesis schemes synthesized in direct or transposed direct form.

20 citations


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

  • ...This problem can be efficiently optimized by B&B MILP [16], [22], [23]....

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Proceedings ArticleDOI
25 May 2003
TL;DR: This paper uses an arithmetic scheme, known as pseudo floating-point (PFP) representation to encode the filter coefficients and shows that the magnitude responses of the filters coded in PFP meet the attenuation requirements of GSM/W-CDMA specifications.
Abstract: The most computationally intensive part of wide-band receivers is the IF processing block. Digital filtering is the main task in IF processing. Infinite precision filters require complicated digital circuits due to coefficient multiplication. This paper presents an efficient method to implement pulse shaping filters for a dual-mode GSM/W-CDMA receiver. 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 filters can be coded using an optimal entropy scheme employing PFP which requires only 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 GSM/W-CDMA specifications.

15 citations


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

  • ...For a multiplierless filter implementation, the hardware complexity increases with the number of the adders, which is proportional to the filter wordlength [2]....

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Dissertation
07 Dec 2016
TL;DR: This thesis presents an ongoing study on Remez-type algorithms for rational approximation problems (which can be used for infinite impulse response (IIR) filter design and the difficulties hindering their robustness), and proposes a (quasi-)optimal approach based on the LLL algorithm which is more tractable than exact approaches.
Abstract: The field of signal processing methods and applications frequentlyrelies on powerful results from numerical approximation. One suchexample, at the core of this thesis, is the use of Chebyshev approximationmethods for designing digital filters.In practice, the finite nature of numerical representations adds an extralayer of difficulty to the design problems we wish to address using digitalfilters (audio and image processing being two domains which rely heavilyon filtering operations). Most of the current mainstream tools for thisjob are neither optimized, nor do they provide certificates of correctness.We wish to change this, with some of the groundwork being laid by thepresent work.The first part of the thesis deals with the study and development ofRemez/Parks-McClellan-type methods for solving weighted polynomialapproximation problems in floating-point arithmetic. They are veryscalable and numerically accurate in addressing finite impulse response(FIR) design problems. However, in embedded and power hungry settings,the format of the filter coefficients uses a small number of bits andother methods are needed. We propose a (quasi-)optimal approach basedon the LLL algorithm which is more tractable than exact approaches.We then proceed to integrate these aforementioned tools in a softwarestack for FIR filter synthesis on FPGA targets. The results obtainedare both resource consumption efficient and possess guaranteed accuracyproperties. In the end, we present an ongoing study on Remez-type algorithmsfor rational approximation problems (which can be used for infinite impulseresponse (IIR) filter design) and the difficulties hindering their robustness.

10 citations

Journal ArticleDOI
Yanfei Cao1, Kai Wang1, Wenjiang Pei1, Yujie Liu1, Yifeng Zhang1 
TL;DR: Simulation results show that the proposed method can effectively and efficiently design high-order SPT filters, including Hilbert transformers and half-band filters with SPT coefficients.
Abstract: Expensive multiplication operations can be replaced by simpler additions and hardwired shifters so as to reduce power consumption and area size, if the coefficients of a digital filter are signed power-of-two (SPT). As a consequence, FIR digital filters with SPT coefficients have been widely studied in the last three decades. However, most approaches for the design of FIR filters with SPT coefficients focus on filters with length less than 100. These approaches are not suitable for the design of high-order filters because they require excessive computation time. In this paper, an approach for the design of high-order filters with SPT coefficients is proposed. It is a two-step approach. Firstly, the design of an extrapolated impulse response (EIR) filter is formulated as a standard second-order cone programming (SOCP) problem with an additional coefficient sensitivity constraint for optimizing its finite word-length effect. Secondly, the obtained continuous coefficients are quantized into SPT coefficients by recasting the filter-design problem into a weighted least squares (WLS) sequential quadratic programming relaxation (SQPR) problem. To further reduce implementation complexity, a graph-based common subexpression elimination (CSE) algorithm is utilized to extract common subexpressions between SPT coefficients. Simulation results show that the proposed method can effectively and efficiently design high-order SPT filters, including Hilbert transformers and half-band filters with SPT coefficients. Experiment results indicate that 0.81N∼0.29N adders are required for 18-bit N-order FIR filters (N=335∼3261) to meet the given magnitude response specifications.

10 citations


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

  • ...However, it should be noted that running MILP on parallel machines generally still requires more computation time than running other techniques on a single processor....

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  • ...There are two types of filter synthesis methodologies, namely, optimal approaches [19, 20] and suboptimal approaches [1, 4, 7, 9, 11, 14, 16, 32, 33, 38]....

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  • ...These include the use of mixed-integer linear programming (MILP) [19, 20], local search techniques [9, 14, 32, 38] and common subexpression elimination (CSE) [5, 6, 10, 12, 29, 31, 36, 37]....

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  • ...For example, MILP requires a few hours of computation time to design filters with length less than 70 when it is solved on a single machine....

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  • ...To tackle that problem, [20] presents a new MILP algorithm on loosely connected parallel machines such as a cluster of workstations....

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References
More filters
Book
01 Jan 1972
TL;DR: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization as mentioned in this paper, which is a standard of graduate-level courses since 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.

4,336 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.

488 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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Journal ArticleDOI
TL;DR: In this article, a digital filter with discrete coefficient values selected from the powers-of-two coefficient space is designed using the methods of integer programming, and the frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients.
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.

451 citations

Journal ArticleDOI
TL;DR: In this article, the remaining unquantized coefficients of a FIR linear phase digital filter when one or more of the filter coefficients takes on discrete values are optimized using the least square response error.
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

191 citations