In this paper, an algorithm is proposed for the design of low complexity linear phase finite impulse response (FIR) filters with optimum discrete coefficients. The proposed algorithm, based on mixed integer linear programming (MILP), efficiently traverses the discrete coefficient solutions and searches for the optimum one that results in an implementation using minimum number of adders. During the searching process, discrete coefficients are dynamically synthesized based on a continuously updated subexpression space and, most essentially, a monitoring mechanism is introduced to enable the algorithm's awareness of optimality. Benchmark examples have shown that the proposed algorithm can, in most cases, produce the optimum designs using minimum number of adders for the given specifications. The proposed algorithm can be simply extended for the optimum design with the maximum adder depth constraint.

Design of Linear Phase FIR Filters With High Probability of Achieving Minimum Number of Adders

Design of hardware efficient FIR filter: A review of the state-of-the-art approaches

Low-cost finite impulse response (FIR) designs are presented using the concept of faithfully rounded truncated multipliers. We jointly consider the optimization of bit width and hardware resources without sacrificing the frequency response and output signal precision. Nonuniform coefficient quantization with proper filter order is proposed to minimize total area cost. Multiple constant multiplication/accumulation in a direct FIR structure is implemented using an improved version of truncated multipliers. Comparisons with previous FIR design approaches show that the proposed designs achieve the best area and power results.

Low-Cost FIR Filter Designs Based on Faithfully Rounded Truncated Multiple Constant Multiplication/Accumulation

In this paper, a novel algorithm is proposed to design sparse FIR filters. It is known that this design problem is highly nonconvex due to the existence of -norm of a filter coefficient vector in its objective function. To tackle this difficulty, an iterative procedure is developed to search a potential sparsity pattern, which is then used to compute the final solution by solving a convex optimization problem. In each iterative step, the original sparse filter design problem is successively transformed to a simpler subproblem. It can be proved that under a weak condition, globally optimal solutions of these subproblems can be attained by solving their dual problems. In this case, the overall iterative procedure converges to a locally optimal solution of the original design problem. The design procedure described above can be repeated for several times to further improve the sparsity of design results. The output of the previous stage can be used as the initial point of the subsequent design. The performance of the proposed algorithm is evaluated by two sets of design examples, and compared to other sparse FIR filter design algorithms.

Peak-Error-Constrained Sparse FIR Filter Design Using Iterative SOCP

In this paper, we present a hardware efficient finite impulse response (FIR) filter design using differential evolution (DE) and common sub expression (CSE) elimination algorithm. With the DE algorithm, we first found a set of filter coefficients with reduced number of signed-power-of-two (SPT) terms without compromising on quality of the filter response. After obtaining coefficients, we applied CSE elimination algorithm, and determined the hardware cost in terms of adders. The filters were designed using DE for various word lengths, and the same were implemented in transposed direct form (TDF) structure. The implemented filters were synthesized in Cadence RTL compiler using UMC 90 nm technology. We compared the performances of our filters with recently best published works in terms of area, delay, power and power-delay-product ( PDP ). One of the proposed filters found to improve a PDP gain of 29% compared to Remez algorithm. The proposed approach showed improvements in filter design for the given specifications.

An approach for FIR filter coefficient optimization using differential evolution algorithm

Digital filters in cascade form enjoy many advantages over their equivalent single-stage realizations in that lower coefficient sensitivity, higher throughput, reduced computational and smaller implementation cost can be achieved. However, the numerical design and optimization of such structure are of much more difficulty than the single-stage case if the filter coefficients are restricted to be of discrete values. This is mainly due to the non-convexity of the constraints, which rules out the possibility of employing sophisticated convex optimization techniques as well as the guaranteed global optimality. In this work, a general-purpose algorithm is proposed for the design of linear phase finite impulse response (FIR) filters in cascade form with discrete coefficients. The proposed algorithm decomposes the overall filter into subfilters during the traverse of a tree search of the overall filter. Discrete-valued linear phase FIR filters are able to be searched and decomposed into both symmetric and non-symmetric subfilters. The optimization complexity is of the same order as the single-stage filter optimization. Design examples have shown that the proposed algorithm is capable of achieving notable reduction in both implementation cost and adder depth compared with their single-stage optimum designs.

Design of Discrete-Valued Linear Phase FIR Filters in Cascade Form

This paper presents a very low-complexity design of variable bandedge linear phase finite-impulse-response (FIR) filters with fixed sharp transition width. The idea is to first decompose the input signal into several channels in the frequency domain. The channel(s) involved with the transition band of the variable filter due to the variation of the bandedge is (are) shaped to produce the required transition band, and then summed up with the channels involved with the passband of the variable filter to produce the required frequency response. The proposed variable filter has extremely low complexity when the transition band is sharp, if compared with other techniques such as the Farrow structure. It is possible that the computational complexity of the variable filter is even lower than that of a corresponding fixed filter with the same transition width and ripple specifications implemented in its direct form.

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Low-Complexity Design of Variable Bandedge Linear Phase FIR Filters With Sharp Transition Band

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.

/pdf/design-of-extrapolated-impulse-response-fir-filters-with-4pm708db6w.pdf

Design of Extrapolated Impulse Response FIR Filters With Residual Compensation in Subexpression Space

Earlier research has shown that filter impulse responses are quasi-periodic and filter coefficients can be approximated by extrapolation techniques. In this paper, a discrete coefficient extrapolated impulse response filter is proposed. Residual compensation technique is introduced to perfectly realize the filter coefficients. Both the extrapolated filter coefficients and the residuals are subexpression encoded to minimize the filter complexity. Numerical example shows that the proposed technique achieves minimum number of adders in the synthesis of the filter when compared with any other existing techniques.

/pdf/subexpression-encoded-extrapolated-impulse-response-fir-1a3ycrp275.pdf

Dong Shi

Papers

Design of Linear Phase FIR Filters With High Probability of Achieving Minimum Number of Adders

Design of Discrete-Valued Linear Phase FIR Filters in Cascade Form

Low-Complexity Design of Variable Bandedge Linear Phase FIR Filters With Sharp Transition Band

Design of Extrapolated Impulse Response FIR Filters With Residual Compensation in Subexpression Space

Subexpression encoded extrapolated impulse response FIR filter with perfect residual compensation