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
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TL;DR: This paper proposes a new hybrid lattice structure, which is not only canonic in the number of multipliers resulting in a significant reduction in overall implementation cost but also exhibits much better FWL properties than the normalized lattICE structure.
Abstract: The excellent finite wordlength (FWL) property of lattice digital filters is well known. The four-multiplier normalized lattice, with signal power at all delay elements normalized to unity, has particular advantage in its overflow property. However, when used to implement an Nth-order digital filter, the normalized lattice implementation requires 5N+1 multipliers. There exists another lattice structure with excellent FWL property called the injected numerator lattice structure. In this paper, we combine the injected numerator lattice and tapped numerator lattice to form a new hybrid lattice structure, which is not only canonic in the number of multipliers resulting in a significant reduction in overall implementation cost but also exhibits much better FWL properties than the normalized lattice structure. An improved “peakedness” measure is also introduced for application where the input signal has a strong time varying sinusoidal component. The new structure requires a few additional adders; it can be used to implement any causal and stable z-transform transfer function. Two numerical examples are presented to demonstrate the performance of the proposed structure.
9 citations
30 Oct 2009
TL;DR: In this paper, an optimization technique is proposed to design the multiplier block with constrained adder depth to achieve low power consumption, and the proposed algorithm generates filters using less adders with low adder depths.
Abstract: A popular technique in the design of multiplierless FIR filters explores the common subexpression sharing when the filter coefficients are optimized. In these techniques, the coefficient multiplier are realized as a multiplier block (MB) with shared shifters and adders. Many researches showed that the power consumption of a MB is often not simply proportional to the number of adders but is rather very much dependent on the adder depth of every coefficient. In this paper, an optimization technique is proposed to design the MB with constrained adder depth to achieve low power consumption. Numerical examples show that the proposed algorithm generates filters using less adders with low adder depth.
8 citations
Cites methods from "Design of discrete-coefficient FIR ..."
...First we review the depth-first search branch and bound algorithm [19]–[21] which has successfully optimized filter coefficients in integer and SPT spaces....
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TL;DR: The focus of this study is a new FIR filter design procedure and to compare this with traditional methods known as the fir2() routine provided by MATLAB.
Abstract: This paper is concerned with the application of forward Orthogonal Least Squares (OLS) algorithm to the design of Finite Impulse Response (FIR) filters. The focus of this study is a new FIR filter design procedure and to compare this with traditional methods known as the fir2() routine provided by MATLAB.
7 citations
TL;DR: In this article, a new design method for linear phase finite impulse response (FIR) filters with discrete coefficients is proposed, where the design problem is formulated as an integer programming problem and solved using ACO.
Abstract: SUMMARY
In this paper, we propose a new design method for linear phase finite impulse response (FIR) filters with discrete coefficients. In a hardware implementation, filter coefficients must be represented as discrete values. The design problem of digital filters with discrete coefficients is formulated as an integer programming problem. But an enormous amount of computational time is required to solve the problem in a strict solver. Recently, ant colony optimization (ACO), a heuristic approach, has been used widely for solving combinational problems such as the traveling salesman problem. In our method, we formulate the design problem as a 0-1 integer programming problem and solve it by using ACO. Several design examples are presented to show the effectiveness of the proposed method.
6 citations
20 May 2012
TL;DR: In this work, a novel genetic algorithm is proposed for the design of multiplierless finite impulse response (FIR) filters with high filter order and wide coefficient wordlength, which outperforms existing algorithms dealing with the similar problems.
Abstract: In this work, a novel genetic algorithm (GA) is proposed for the design of multiplierless finite impulse response (FIR) filters with high filter order and wide coefficient wordlength. GA mimics the nature evolution to optimize complicated problems and in theory optimum solutions can be obtained with infinite computation time. However, in practical filter design problem, when the filter specification is stringent, requiring high filter order and wide coefficient wordlength, GA often fails to find feasible solutions, because the discrete search space thus constructed is huge and 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 of the small space is constructed surrounding an optimum continuous solution with a floating passband gain. This increases the chances for the GA to find feasible solutions, but not sacrificing the coverage of the search space. In addition, the search in the multiple spaces can run in parallel, and thus the computation time for the design of filters under consideration reduces significantly. Design examples show that the proposed GA outperforms existing algorithms dealing with the similar problems.
5 citations
Cites background from "Design of discrete-coefficient FIR ..."
...Although mixedinteger linearing programming (MILP) based algorithms has been developed for parallel optimization of FIR filters with signed power of two coefficients [20], the programming and the partitioning of the problems are complicated, and therefore, no attempts have been made for the design of the filters sharing add-shift network among coefficients....
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References
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Book•
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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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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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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
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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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