FIR digital filter design techniques using weighted Chebyshev approximation

This paper discusses the various approaches to designing FIR digital filters using the theory of weighted Chebyshev approximation. The different design techniques are explained and compared on the basis of their capabilities and limitations. The relationships between filter parameters are briefly discussed for the case of low-pass filters. Extensions of the theory to the problems of magnitude and complex approximation are also included, as are some recent results on the design of two-dimensional FIR filters by transformation.     

Complex Chebyshev approximation for FIR digital filters

An adaptive approach to FIR (finite impulse response) filter design is applied to a fully general complex specification, showing it to be capable of giving an optimum Chebyshev solution. It is thought to be one of the first practical approaches to achieve this in the case of a complex function. Design examples include a bandpass filter with nearly linear phase and all-pass filters with general shaping phase. Comparisons are drawn with equivalent results from other algorithms     

A new method for higher-order linear phase FIR digital filter using shifted Chebyshev polynomials

In this work, a new method for the design of linear phase finite impulse response (FIR) filters using shifted Chebyshev polynomial is proposed. In this method, magnitude response of FIR filter is approximated with the help of shifted Chebyshev polynomials. The number of polynomials used for approximation depends upon the order of filter. Design problem of filter is constructed as minimization of integral mean-square error between the ideal response and actual response through differentiating it with respect to its coefficients, which leads to a system of linear equations. The simulation results included in this paper show the efficiency of proposed method. It is also evident from the results that the proposed method is suitable for higher filter taps.     

一种基于FPGA的分布式FIR数字滤波器设计

在宽带中频软件无线电台收发系统中,由于FIR滤波器具有良好的线性相位特性及实现的灵活性,通常将它作为数字上下变频中的整形低通滤波器.本设计采用altera公司的CycloneⅡ系列中的EP2C20Q240C8芯片,以一个8阶分布式算法的FIR低通数字滤波器电路为例,其主要通过LUT、加法器和移位寄存器实现.最后对该分布式算法进行了仿真验证.结果表明,该优化结构高效合理地利用FPGA硬件资源,可有效应用于高性能中频数字电台的信号处理模块.     

A programmable FIR digital filter using CSD coefficients

An area-efficient programmable FIR digital filter using canonic signed-digit (CSD) coefficients was implemented that uses a switchable unit-delay to allocate the desired number of nonzero CSD coefficient digits to each filter tap. The prototype chip can allocate up to 16 pairs of nonzero CSD coefficient digits for a linear-phase filter, thus realizing filters with 32 linear-phase taps operating at 180 MHz with two nonzero CSD digits per filter tap. Additional nonzero CSD digits can be allocated to filter taps at the penalty of a reduced filter length and a reduced data-rate. The chip was implemented with 16-bit I/O in a die size of 5.9 mm by 3.4 mm using 1.0-μm CMOS technology     

Quantized FIR filter design using compensating zeros

This article presents a design method for translating a finite impulse response (FIR) floating-point multiplierless filter design. Conventional wisdom dictates that finite word-length (i.e., quantization) effects can be minimized by dividing a filter into smaller, cascaded sections. In this design method, it is shown how to quantize the cascaded sections so that the finite word-length effects in one section are guaranteed to compensate for the finite word-length effects in the other section. This simple method called, "compensating zeros," ensures that: (1) the quantized filter's frequency response closely matches the unquantized filter's frequency response (in both magnitude and phase); and (2) the required hardware remains small and fast.     

Constrained Chebyshev design of FIR filters

In many filter-design problems, additional constraints are often imposed on the optimal filter in the sense of, say, minimal Chebyshev error norm. Based on the characteristic properties of the optimal filter for the Chebyshev design with frequency equation constraints, a modified Remez (MRemez) algorithm is proposed in this paper. The central problem of this paper is the constrained Chebyshev design of finite-impulse response filters with equation and inequality constraints in the frequency domain. By converting the problem into a series of Chebyshev design problems with equation constraints, an iterative MRemez algorithm which uses the MRemez algorithm as the computational core of the iteration is proposed, and the convergence of the algorithm is obtained. Design examples demonstrate the effectiveness and the fast convergence of the MRemez algorithm and the iterative MRemez algorithm.     

Simplified weighted least squares design of 2-D FIR digital filters

A simple easy to use and very flexible approach is presented for the design of 2-D fir digital filters. It is illustrated by two examples, a rectangular filter and a diamond filter. Appropriate selection of the weighting function which is used in the weighted least squares method can yield very diverse characteristics, like the possibility to meet specifications on both frequency response and step response.     

数字滤波器性能指标优化中FIR的设计与仿真研究

数字滤波器,通俗来讲,就是一种算法或者装置,一般情况下由数字乘法器、加法器和延时单元3部分构成。对数字滤波器的设计方法研究已有20年的历史,目前其正处于稳定发展时期。遗传算法等优化算法的利用,在优化数字滤波器的性能指标以及仿真实现FIR数字滤波器方面进行得如火如荼。这种基于生物界自然选择和进化机制发展的算法具有并行度高、随机、自适应搜索等特点,当前在组合优化、生产调度、自动控制、图像处理、机器学习、数据挖掘等各个方面均有所应用。正如人们所理解的,数字信号处理就是从噪声中寻找有用的信号,恰巧这也是寻找最优解的过程。可以说,在数字滤波器设计方面,遗传算法是一个大胆的尝试。所以,文章针对数字滤波器性能指标优化中FIR的设计与仿真进行了研究。     

Multiplier-less FIR filter design using a genetic algorithm

A new synthesis technique is described for multiplier-less FIR digital filters consisting of a cascade of primitive linear phase sections. For medium-order filters the search space for an optimal cascade is typically of the order of 10³⁰ and this can be examined in a computation efficient way using the parallel-search capability of a genetic algorithm (GA). A particular form of GA based upon multilevel or structured chromosomes has been developed for the primitive cascade problem. Initial results suggest that, for the cost of increased filter delay, a typical 2:1 advantage can be achieved in both VLSI chip area and clock rate compared to filters designed using the usual equiripple method     

基于Verilog HDL的FIR数字滤波器的优化设计与仿真

对FIR数字滤波器基于Verilog HDL的实现进行了研究,在分布式算法的基础上进行了改进,设计了32阶常系数FIR滤波器。用Verilog硬件描述语言进行数字逻辑设计,使用Synopsys VCS作为仿真工具对设计进行仿真和验证,在Synopsys公司的Design Compiler下进行综合。结果表明,该设计既保证了运行速度又节省了芯片的面积,可以广泛应用于数字集成电路的设计中。     

A weighted least squares algorithm for quasi-equiripple FIR and IIRdigital filter design

It has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of a finite impulse response (FIR) filter, the weighted least squares solution is equiripple. The crux of the problem lies in the determination of the necessary least squares frequency response weighting function. A novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi-equiripple design is presented. The algorithm converges very rapidly. It typically produces a design which is only about 1 dB away from the minimax optimum solution in two iterations and converges to within 0.1 dB in six iterations. Convergence speed is independent of the order of the filter. It can be used to design filters with arbitrarily prescribed phase and amplitude response     

In the optimum design of the block adaptive FIR digital filter

A general optimum block adaptive (GOBA) algorithm for adaptive FIR (finite impulse response) filtering is presented. In this algorithm, the correction terms for the filter coefficients in each block, instead of the convergence factors, are optimized in a least squares sense. There are no constraints on the block length L and the filter tap number N. It is shown that the GOBA algorithm is reduced to the normalized LMS algorithm when L⩾N. The convergence of the GOBA algorithm can be assured if the correlation matrix of the input signal is positive definite. Computer simulations based on an efficient computing procedure confirm that the GOBA algorithm achieves faster convergence with slightly degraded convergence accuracy in stationary environments and better weight tracking capability in nonstationary environments as compared to existing block adaptive algorithms with no constraints on L and N     

基于FPGA的FIR滤波器的性能研究

目前FIR滤波器的一般设计方法比较繁琐,开发周期长,如果采用设计好的FIR滤波器的IP核,则开发效率大为提高。本方案基于Altera公司的Cyclone Ⅱ系列芯片EP2C8Q208C8N,首先利用MATLAB中的滤波器函数fir2得出需产生的FIR滤波器的系数,再导入FIR IP Core,成功完成了FIR数字滤波器的设计。另外分析了阶数与不均匀采样数据对FPGA资源的影响和对生成FIR滤波器的输出性能的影响,并将实际输出的幅频特性图与我们需要的幅频特性图相比较,验证生成的FIR数字滤波器的性能。     

基于FPGA和Matlab的FIR数字滤波器

为了满足信号处理快速和灵活的要求,基于FPGA实现的FIR滤波器有这两方面的优势,使用Matlab中的FDATool计算出滤波器系数并分析其幅频特性,利用FPGA分别设计实现串行结构、全并行结构以及基于IP核的FIR数字滤波器。利用Matlab软件进行FIR滤波器仿真,并与基于FPGA实现滤波器的Modelsim仿真输出数据进行比较,结果表明,设计的FIR滤波器功能正确、滤波性能良好。通过对不同结构滤波器的资源占用情况和数据处理速度进行分析,得出不同应用场合可选择不同的滤波器结构的结论。     

I.I.R. digital filter design using constrained optimisation techniques

A new design method for all-pole infinite impulse response (i.i.r.) digital filters is introduced. The method involves minimising the area between the ideal lowpass filter response in the passhand and the actual passband response, subject to a quadratic constraint which ensures filter realisability. A unique solution is obtained to the minimisation which relates the filter weights to the eigenvector of a Toeplitz matrix. The filters are seen to have a small ripple in the passhand and a sharp cutoff in the stopband.     

FIR数字滤波器的最优化设计及MATLAB实现

尽管窗函数法与频率抽样法在FIR数字滤波器的设计中有着广泛的应用,但两者都不是最优化的设计。介绍了一种基于等波纹切比雪夫逼近准则的FIR数字滤波器的最优化设计方法,通过MATLAB的仿真实现,证明了该方法是一种最优化的设计。     

Two-dimensional FIR compaction filter design

The design of signal-adapted multirate filter banks has been an area of research interest. The authors present the design of a 2-D finite impulse response (FIR) compaction filter followed by a 2-D FIR filter bank that packs the maximum energy of the input process into a few subbands. The energy compaction property of the 2-D compaction filter is extremely good for higher filter orders and converges to the ideal optimal solution as the order tends to infinity. The design procedure is very straightforward and involves a 2-D spectral factorisation     

FIR数字滤波器的设计与实现

以窗函数法设计FIR数字滤波器,利用MATLAB工具软件辅助设计和仿真,对信号进行低通滤波,并使用CCS应用软件进行仿真及调试,实现了DSP下数字低通滤波器的设计.