Weighted least-square design of FIR filters using a fast iterative matrix inversion algorithm

Chapter 2 - Design and Implementation of Digital FIR Filters

Optimisation based design of finite impulse response (FIR) filters has been an active area of research for quite some time. The various algorithms proposed for FIR filter design aim at meeting a set of desired specifications in the frequency domain. Evolutionary algorithms have been found to be very effective for FIR filter design because of the non-linear, non-differentiable and non-convex nature of the associated optimisation problem. The present work proposes two modified versions of a recently developed evolutionary technique i.e. artificial bee colony (ABC) algorithm for design of FIR filters. The applicability of the proposed approach has been evaluated by comparing its response with conventional reported filter design techniques. The proposed variants of ABC are found to outperform other non-convex algorithms in achieving the desired specifications. In addition to the simulation results, the designed filters have been implemented in hardware using Xilinx-xc7vx330t-3ffg1157 (Virtex-7) field programmable gate array. The hardware implementation allows validation of the proposed techniques for practical filtering applications by considering real time operation parameters.

To enhance the efficiency of designing finite impulse response (FIR) filters with a controllable cut-off frequency that possess excellent transfer characteristics, this paper proposes a closed-form filter design based on transfer characteristic compensation. First, a novel filter design based on a convolution window is presented, and the relationship between the spectrum of this window and the filter performance is elaborated. We then derive a three-stage filter design scheme that describes the design of an irregular filter, design of a compensation filter and filter summation. This scheme can be simplified into a closed-form design characterized by two analytic formulas by merging the intermediate steps. The configuration of a vital Kaiser window parameter is also derived. Numerical results show that the proposed closed-form design accurately controls the cut-off frequencies and exhibits a transfer performance comparable to the Remez design and the closed-form weighted least square (WLS) design. Moreover, our method is more efficiency than the closed-form WLS method for the design of high-order FIR filters.

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.

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.

The design of Finite Impulse Response (FIR) digital filter involves multi-parameter optimization, while the traditional gradient-based methods are not effective enough for precise design. The aim of this paper is to present a method of designing 24th order high pass FIR filter using an evolutionary heuristic search technique called Weight Improved Particle Swarm Optimization (WIPSO). A new function of the weight parameters is constructed for obtaining a better optimal solution with faster computation. The performance of the proposed algorithm is compared with two other search optimization algorithms namely standard Genetic Algorithm (GA) and conventional Particle Swarm Optimization (PSO). The simulation results show that the proposed WIPSO algorithm is better than GA and PSO in terms of the magnitude response accuracy and the convergence speed for the design of 24th order high pass FIR filter.

SummaryThis work presents the design of an asynchronous digital finite impulse response (FIR) filter suitable for high‐performance partial response maximum likelihood (PRML) read channel ICs. A high throughput, low latency FIR filter is the basic requirement for the equalization process in read channels. To achieve the enhancement in speed and reduction in latency of the FIR filter, its computational units are deeply pipelined using high‐capacity hybrid (HC‐hybrid) logic pipeline method. The designed FIR filter has been simulated using UMC‐180 nm and UMC‐65 nm technologies. Simulation results show that the asynchronous digital FIR filter can operate up to a throughput of 1.17 Giga items/s in 180 nm and 2.3 Giga items/s in 65 nm technology yet with the latency in the order of ns.

In this communication, one novel attempt has been made towards the design of minimum-phase finite impulse response (FIR) filter using one evolutionary computation technique, named differential evolution (DE) algorithm. Mean square error (MSE) between the frequency samples of the ideal filter and the designed filter in the pass-band and stop-band region and the minimum average error (MAE) between the frequency samples in the transition-band region had been considered for the formulation of the objective function in the optimization process. Performance of the optimization technique has been monitored in terms of convergence characteristics for four different orders of FIR filter under consideration. Robustness of our proposition has been firmly established in the sense that the proposed algorithm can be suitably tuned for the design of low-pass, high-pass or band-pass FIR filter of different specifications. Supremacy of the proposed algorithm over other existing techniques for the design of minimum-phase FIR filter has been substantiated by means of frequency response and pole-zero diagrams.

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

Background/Objectives: FIR filters play a vital role in signal processing applications. This research work presents a low power and high speed efficient buffer based Distributed Algorithms and it is analyzed with Electro Cardio Gram (ECG) signal Finite Impulse Response (FIR) filter design. Methods/Statistical Analysis: The proposed FIR filter is designed using buffer based DA and it is simulated and synthesized using Cadence digital labs. This is compared with different architectures such as conventional DA, separated look up table DA and LUT less DA. Findings: Synthesis report shows that the proposed design has 52% less power dissipation compared with the conventional DA, 21% reduction in delay with separated Look Up Table (LUT) DA and 8% reduction in area with LUT less DA. Conclusion/Improvements: Presently this method is applied for ECG signal input with 16-tap FIR filter. This can be extended for higher order filters to achieve better performance.

This paper presents a novel approach for the design of two-dimensional (2D) Finite Impulse Response (FIR) filters. The design of FIR filters is generally non-differentiable, multimodal and higher dimensional; especially for 2D filters. A large number of filter coefficients are optimized either using constrained or unconstrained optimization approach. Due to the large number of constraints, traditional design methods cannot produce optimal filters required for some crucial applications. This makes meta-heuristic algorithms as good alternatives for addressing such constraints more efficiently. In order to improve the performance of 2D filters, we propose an Accelerated Artificial Bee Colony algorithm, termed as AABC algorithm. The earlier reported ABC based methods perform the modification of a single parameter of the solution in each cycle. But in this proposed AABC algorithm, we have adopted multiple parameters change of search equation at each step. This in turn improves the convergence speed of the algorithm by three times than the classical ABC algorithm and two times with respect to recently developed CABC method. In order to achieve better exploration behaviour of abandoned bees, we have also introduced a change during the initialization strategy of scout bees in the proposed AABC algorithm. The efficiency and robustness of the proposed algorithm are demonstrated by comparing its performance with classical Genetic Algorithm (GA), Particle Swarm Optimization , ABC and CABC methods.

A novel procedure that makes use of the maximum entropy method (MEM) for the design of linear-phase FIR (finite impulse response) digital filters is described. It is shown that, by applying MEM to the inverse of the desired gain function or its square root function, it is possible to generate linear-phase FIR filters that match the given gain function to any desired degree of accuracy. Moreover, an iterative algorithm makes the design procedure very efficient, since the higher-order filters can be recursively generated from the lower-order ones. To minimize the effect of any residual passband distortion, a final averaging scheme on the lower-order filters generates a class of passband distortion-free linear-phase FIR filters. The new filters are seen to be more robust to changes in transition bandwidth as well as stopband level. Simulation results that compare the present procedure with other well-known methods are also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The design of high-speed FIR (finite impulse response) filters using switched-current technology is considered. By using current to represent signals, an FIR filter has been implemented using building blocks developed from switched-current circuits. It has been fabricated using the MOSIS 2- mu m CMOS technology, and can operate at a sampling frequency over 10 MHz. >

The use of optimization techniques for designing digital filters has become widespread in recent years. Among the techniques that have been used include steepest descent methods, conjugate gradient techniques, penalty function techniques, and polynomial interpolation procedures. The theory of linear programming offers many advantages for designing digital filters. The programs are easy to implement and yield solutions that are guaranteed to converge. There are many areas of finite impulse response (FIR) filter design where linear programming can be used conveniently. These include design of the following: filters of the frequency sampling type; optimal filters where the passband and stopband edge frequencies of the filter may be specified exactly; and filters with simultaneous constraints on the time and frequency response. The design method is illustrated by examples from each of these areas.