Hardware-Efficient Parallel FIR Filter Structure Based on Modified Cook-Toom Algorithm

Digital filters play a central role in modern Digital Signal Processing (DSP) systems. Finite Impulse Response (FIR) filters can provide solutions with guaranteed stability and linear phase. However, the main disadvantage of conventional FIR filter designs is that they become computationally complex, especially in applications demanding narrow transition bandwidths. Therefore, designing FIR filters with very stringent specifications and a low complexity is currently an important challenge. In this chapter, a review of the recent methods to efficiently design low-complexity linear-phase FIR filters is presented. The chapter starts with an introduction to linear-phase FIR digital filters. Then, an overview of the design methods that have been developed in literature to design low-complexity FIR filters is presented. Finally, the most common and recent of these methods along with their corresponding special structures are explained.

Digital filters play a central role in modern digital signal processing (DSP) systems. Finite impulse response (FIR) filters can provide solutions with guaranteed stability and linear phase. However, the main disadvantage of conventional FIR filter designs is that they become computationally complex, especially in applications demanding narrow transition bandwidths. Therefore, designing FIR filters with very stringent specifications and a low complexity is currently an important challenge. In this chapter, a review of the recent methods to efficiently design low-complexity linear-phase FIR filters is presented. The chapter starts with an introduction to linear-phase FIR digital filters. Then, an overview of the design methods that have been developed in literature to design low-complexity FIR filters is presented. Finally, the most common and recent of these methods along with their corresponding special structures are explained.

Recursive structures are introduced for implementing long linear-phase finite impulse response (FIR) filters using a very small number of multipliers. The implementation uses the principle of switching and resetting between two identical copies of the same infinite impulse response (IIR) filter. The impulse response of the resulting filters is a truncated and shifted version of the response of a filter G(z)G(z/sup -1/) where G(z) is a stable IIR stable and G(z/sup -1/) is the corresponding unstable IIR filter. The filters are implemented as a parallel connection of several branches, each branch generating a truncated response corresponding to a complex conjugate pole pair and its mirror-image pair. The truncation is performed using a feedforward term which provides pole-zero cancellations. To stabilize the pole-zero cancellations, and to avoid the quantization error from growing too much, the branch filters are implemented by applying the principle of switching and resetting. It is shown, by means of an example, that by using this approach a nearly optimum FIR filter of order larger than 500 using just 17 adjustable parameters can be designed. >

It was shown by P.P. Vaidyanathan (1993) that in the case of orthonormal and biorthonormal filter banks one can convolve two signals x(n) and g(n) by directly convolving the subband signals and combining the results. In the present work, this result is further generalized. The coding gain for a biorthonormal convolver is also derived. As an application, a novel low-sensitivity FIR (finite impulse response) filter structure is derived from the convolution theorem. This FIR filter structure is shown to be attractive when the filter coefficients are quantized to low bit rate. For a fixed word length implementation, the deterministic coding gain over direct convolution for the cases of quantizing the input signal and filter coefficients is considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

PurposeTraditionally, each time a new design for a finite impulse response (FIR) filter is required, a new algorithm has to be developed specially for the FIR filter. Furthermore, corresponding hardware architecture must be designed specially to meet the requirement of the FIR specifications. The purpose of this paper is to propose an arithmetic logic unit (ALU)‐based universal FIR filter suitable for realization in field programmable gate arrays (FPGA), where various FIR filters can be implemented just by programming instructions in the ROM with identical hardware architecture.Design/methodology/approachRather than multiplier‐accumulator‐based architecture for conventional FIR, the proposed ALU architecture implements the FIR functions by using accumulators and shift‐registers controlled by the instructions of ROM. Furthermore, time division multiplexing access (TDMA) technique is employed to reduce the chip size. In addition, the proposed FIR architecture is verified in a SOC hardware and/or software co‐emulation system.FindingsAn ALU‐based universal FIR filter suitable for realization in FPGA is designed and verified in a SOC hardware/software co‐emulation system with example of a 64‐tap FIR filter design.Originality/valueA software‐based design method as well as TDMA scheme for the ALU‐based FIR filter are introduced, making FIR filter architecture universal, programmable, and consuming less FPGA resources.

Cascaded warped-FIR and FIR filter structure for loudspeaker equalization with low computational cost requirements

WITHDRAWN: An Optimistic Design of 16-Tap FIR Filter with Radix-4 Booth Multiplier Using Improved Booth Recoding Algorithm

&lt;span&gt;The main purpose of this paper is to design a two-dimensional digital finite impulse response (FIR) filter using data broadcast and non-broadcast structure. The implementation of two-dimensional digital FIR filter is done using very high speed integrated circuit hardware description language (VHDL). Rectangular window method is used for calculating 2D digital FIR filter coefficients for data broadcast and non-broadcast structure. The coefficients of the one-dimensional digital FIR filter are obtained using the MATLAB filter design and analysis (FDA) tool for two different cut-off frequencies and are multiplied to get the necessary coefficient for the two-dimensional FIR filter to be designed; the simulation is done on Artix-7 series field programmable gate array (FPGA), target device (xc7a35t-cpg236) using Vivadov.2015.2. The proposed design reduces the area utilization and the power consumption when compared with the existing literature. The experimental result shows that the power consumption is improved by 97% and there is an improvement of 24% in area utilization for the two-dimensional with and without data broadcast one dimensional FIR filter structures.&lt;/span&gt;

An Finite Impulse Response (FIR) filter is a widely used digital filter technology whose impulse response has a finite duration. An FIR filter is usually favored for many reasons such as easy to design, easy to implement on a variety of system architectures. An FIR filter can be easily designed with a linear phase response and its output is more predictable since it doesn't have feedback components. There are both engineer and mathematical methods for designing an FIR filter so that machine learning doesn't play an important role in the FIR filter design. In this paper, we present an alternative to traditional filter design methods to direct learn the FIR filter coefficients from input data with machine learning algorithm. With the proposed algorithm, we can easily design an FIR filter from the input data mixed with designed all spectrum noise signal. To show the capability of this algorithm, an example application of suppressing background music from speech or vice versa is demonstrated in this paper. Despite that the music and speech have a lot of overlap in their spectrum, the filter designed by our algorithm can successfully suppress music or speech in a mixture of music and speech signals.

ABSTRACTAn original analytical method, based on modified Christoffel–Darboux formula, is used in the paper in order to synthesise a linear-phase band-pass finite impulse response (FIR) filter function that can have an effect of Hilbert transformer. New structure of the band-pass FIR filter in recursive realisation, together with the corresponding difference equation, is presented providing the efficient filter solution without multipliers. Several examples of filter types for different parity of two real free integer parameters, including a particular solution of Hilbert transformer, are considered in terms of required number of adders and values of cut-off frequencies of the pass and stop bands. A comparison of the proposed band-pass filter characteristics with those of a classical filter solution is provided in the paper.

This paper considers the design of computationally efficient narrow-band linear-phase finite-impulse response (FIR) filters with the transfer function of the form H(z) = F(z/sup M/)G(z), where F(z) is a linear-phase FIR transfer function. G(z) is constructed as a cascade of two linear-phase multiplier-free FIR filter building blocks. The first blocks are of the form 2/sup -P//sub r/[1-z/sup -K//sub r//(1-z/sup -1/) with different values of the integers K/sub r/. In these blocks the P/sub r/'s are integers. The second blocks are of the form ( 1/2 )(1 + z/sup -L//sub r/) with different values of the integer L/sub r/. Given the filter specifications, the problem is to find these building blocks, the order of F(z), and the integer M in F(z/sup M/) and to optimize the impulse-response values of F(z) so that the arithmetic complexity is minimized. It is shown how F(z) can be conveniently optimized with the aid of the fast Remez multiple exchange algorithm. For multiplier-free designs, the overall filter should exceed the given criteria in order to enable one to quantize the coefficient values of F(z/sup L/) to have two powers-of-two representations. Two examples taken from the literature show that the optimized proposed filters outperform other existing filter designs meeting the same criteria.

The weighted least square (WLS) design of two-dimensional (2-D) linear-phase finite impulse response (FIR) filters with quadrantally symmetric or anti-symmetric magnitude responses is studied in this paper. Firstly, the necessary and sufficient condition for minimizing the WLS error is obtained in the form of matrix equation. Based on the matrix equation, a novel algorithm is derived for the WLS design of 2-D filters with two-valued weighting functions. Further, convergence of the algorithm is established and the computational complexity is analyzed. Because the new algorithm deals with the filter parameters in their natural 2-D form and the transition band is not sampled, the amount of computation required is reduced significantly, especially for high order cases. Finally, examples are presented to illustrate the performance of the proposed algorithm.

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.

This correspondence presents a novel approach for the design of two channel perfect reconstruction (PR) linear phase finite-impulse response (FIR) filter banks. A broad class of even and odd filter length PR filter bank cases can be obtained by simply reordering an appropriate cascade form synthesizing the polyphase components of a linear phase FIR filter.

The approximation problem of a filter function of even and odd order is solved mathematically in this paper most directly applying the proposed Christoffel-Darboux formula for two continual orthogonal polynomials on the equal finite segment. As a result, a linear phase digital finite impulse response (FIR) filter function is generated in compact explicit form. In addition, a new difference equation and structure of linear phase digital FIR filter are proposed. Two examples of the extremely economic FIR filter (with four adders and without multipliers) designed by the proposed technique are presented. The proposed solutions are extremely efficiency in regard to energy consumption.DOI: http://dx.doi.org/10.5755/j01.eee.18.8.2639