A design algorithm for optimal low-pass nonlinear phase FIR digital filters

The transfer function of the low-pass nonlinear phase finite impulse response (NLPFIR) digital filter is decomposed into a nonlinear phase part and a linear phase part. An algorithm is proposed to iteratively design the magnitude of the linear phase part and the squared magnitude of the nonlinear phase part by directly calling the Remez algorithm of McClellan, et al. [1]. In the design of the nonlinear phase part, we assume that the linearity constraint on the phase is dropped but the phase response is not specified. A scheme is incorporated into our algorithm so that it can design the filter with the desired ripple ratio. This approach also leads to a method for finding the minimum ripple ratio for the given orders of the two parts and band edges of the filters. The filters with ripple ratio larger than this minimum value can be designed by our algorithm and neither passband nor stopband ripples are required to be prescribed. Analysis of roundoff noise reveals that the cascade filter implementation usually needs higher wordlengths than its direct for counterpart for the same roundoff noise performance.     

A new procedure for the design of high order minimum phase FIR digital or CCD filters

The approximation problem for high-order minimum phase FIR filter is solved without requiring any polynomial factorization. A modified Parks-McClellan program is used to compute the amplitude function; the minimum phase function is then derived by a method using the FFT algorithm. The procedure is illustrated by the design of various high order filters; short computation time with no numerical troubles is achieved.     

Design of linear phase FIR filters using fractional derivative constraints

In this paper, the designs of linear phase FIR filters using fractional derivative constraints are investigated. First, the definition of fractional derivative is reviewed briefly. Then, the linear phase FIR filters are designed by minimizing integral squares error under the constraint that the ideal response and actual response have several same fractional derivatives at the prescribed frequency point. Next, the fractional maximally flat FIR filters are designed by letting the number of fractional derivative constraints be equal to the number of filter coefficients. Finally, numerical examples are demonstrated to show that the proposed method has larger design flexibility than the conventional integer derivative constrained methods.     

Design techniques for high-speed multirate multistage FIR digital filters

This paper presents architecture design techniques for implementing both single-rate and multirate high-speed finite impulse response (FIR) digital filters, with emphasis on the multirate multistage interpolated FIR (IFIR) digital filters. Well-known techniques to achieve high-speed and low-power applications for the single-rate digital FIR architecture are summarized, followed by the introduction of variable filter order selection, optimal filter decomposition, memory-saving and mirror symmetric filter pairs techniques which offer further gains in both performance and complexity reduction for the multirate multistage digital FIR architecture. A filter design example with TSMC 0.25?µm standard cell for 64-QAM baseband demodulator shows that the area is reduced by 39% for low-complexity application. Moreover, for high-speed application, the chip can operate at 714?MHz. Finally, a designed decimator which is used in the CDMA cellular shows that the area is reduced by 70% as compared with conventional approach.     

可规划相位FIR滤波器的神经网络设计方法

本文针对可规划相频响应的实系数FIR滤波器的逼近问题,采用一个三层复激活函数前馈神经网络来实现。该网络隐层各神经元的激活函数为复指数函数,将滤波器系数作为隐层各神经元到输出层的连接权值,通过对误差函数的最小化来调整权值,并根据网络特性与所要设计的滤波器的特点,提出了一些实际设计中训练样本集选取与误差加权值设置的规则。依托所采用的神经网络,根据上述规则,进行了两例可规划相频特性的实系数FIR滤波器的设计,结果表明所设计滤波器的相频响应较好地满足了设计要求。     

1D and 2D economical FIR filters generated by Chebyshev polynomials of the first kind

Christoffel–Darboux formula for Chebyshev continual orthogonal polynomials of the first kind is proposed to find a mathematical solution of approximation problem of a one-dimensional (1D) filter function in the z domain. Such an approach allows for the generation of a linear phase selective 1D low-pass digital finite impulse response (FIR) filter function in compact explicit form by using an analytical method. A new difference equation and structure of corresponding linear phase 1D low-pass digital FIR filter are given here. As an example, one extremely economic 1D FIR filter (with four adders and without multipliers) is designed by the proposed technique and its characteristics are presented. Global Christoffel–Darboux formula for orthonormal Chebyshev polynomials of the first kind and for two independent variables for generating linear phase symmetric two-dimensional (2D) FIR digital filter functions in a compact explicit representative form, by using an analytical method, is proposed in this paper. The formula can be most directly applied for mathematically solving the approximation problem of a filter function of even and odd order. Examples of a new class of extremely economic linear phase symmetric selective 2D FIR digital filters obtained by the proposed approximation technique are presented.     

最小平方误差受限的FIR滤波器设计

在设计FIR滤波器时,往往会指定过渡带大小,但过渡带的引入只是为了便于滤波器的设计,而并不是物理上的需要,所以在设计中仅需指定截至频率。这是第一个设计理念。此外,在FIR滤波器的设计中存在两种准则:一是等波纹设计准则 (即最大误差最小化或者Chebyshev准则 ),另一种是平方误差最小准则。但在现实中两种准则往往要同时兼顾,所以仅基于其中一种准则来设计不能得到最佳结果。这是第二个设计理念。基于上述两种设计理念,提出了一种新的FIR滤波器设计算法。该算法采用最陡梯度下降法来对平方误差最小化下的最佳滤波器系数进行迭代修正,得到最佳结果。     

基于雷米兹交换算法设计线性相位对数FIR滤波器

根据线性相位对数FIR滤波器幅度响应与线性相位FIR滤波器幅度响应的关系 ,将线性相位对数滤波器设计转换为线性相位FIR滤波器设计。该方法直接采用雷米兹交换算法即可获得线性相位对数滤波器通带和阻带的等纹波特性。另外 ,该方法既可基于频域均匀采样也可基于频域非均匀采样 ,具有一定的通用性和灵活性     

1D linear-phase band-pass multiplierless FIR Hilbert transformers and filters

An 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.     

Analysis and optimal realization of pole-zero sensitivity for FIR digital filters

Aiming at the deviation of pole and zero in filters which caused by the finite word length (FWL) effects,the sensitivity of pole and zero for FIR digital filters to coefficient errors was studied based on the state-space model.Unlike the IIR filter,the system matrix in state-space model of the FIR filter was defective.A set of generalized eigenvectors of defective matrix was introduced to analyze the pole sensitivity and derive the measure expression,and optimal realizations with respect to pole-zero sensitivity for FIR filters were proposed by finding optimal transformation matrices according to the similarity transformation theory.Theoretical analysis and simulation experiments show that the poles of a FIR filter are more sensitive to coefficient errors,and the proposed optimal realizations can reduce the sensitivity.     

Relations between thek-dimensional unconstrained and linear phase FIR Wiener filters

In this note, we show that thek-dimensional linear phase FIR Wiener filter can be obtained from the unconstrained filter with a simple reverse and add operation. The relation between the linear phase and unconstrained phase filters is obtained also in the case of a multichannelk-dimensional system. In this case, the properties of the autocorrelation matrix do not allow the simplifications noted for the single channel case.     

A new closed form method for design of variable bandwidth linear phase FIR filter using different polynomials

In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response (FIR) filters using different polynomials such as shifted Chebyshev polynomials, Bernstein polynomials and shifted Legendre polynomials is proposed. For this purpose, the transfer function of a variable bandwidth filter, which is a linear combination of fixed-coefficient linear-phase filters and the above polynomials are separately exploited as tuning parameters to control bandwidth of the filter. In order to determine the filter coefficients, mean squared difference between the desired variable bandwidth filter and the practical filter is minimized by differentiating it with respect to its coefficients leading to a system of linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, which reduces the computational complexity. Several examples are included to demonstrate effectiveness of the proposed method in terms of passband error (e_p), stopband error (e_s) and stopband attenuation (A_s).     

Method for FIR filters design with compressed cosine using Chebyshev's norm

This paper considers a new method for FIR filters design. The method uses an L_∞ optimality norm. To achieve a better approximating effect, a new modulating function which compresses the oscillations of the cosine is proposed. A parameter sets the gradient of the modulating function, with respect to the oscillations’ compression. The approximating polynomial is carried out using Remez’ exchange algorithm. An optimal polynomial with lowest possible (four) degree, that approximates an ideal filter's response with high precision is proposed. With the proposed method a FIR filter with arbitrary specifications can be designed. Design examples of FIR filters with a minimization of calculation are performed. The obtained filter's responses are close to the ideal response. The design examples demonstrate that the proposed approach may be a good alternative in several applications.     

基于FPGA的FIR滤波器的设计与实现

分析了FIR滤波器的结构特点和基本原理，基于Matlab用窗函数法对FIR滤波器进行设计，并在Sireulink中进行系统仿真。最后，在FPGA中实现并利用SignalTap Ⅱ逻辑分析器对设计进行测试验证，测试结果与仿真结果一致。     

基于线性相位FIR滤波的三维曲面的光学检测

利用一组规则机线投影到物体表面的畸变光珊，采用线性相位ＦＩＲ滤波技术解调出含有物体表面高度信息的相位。建立了一种较二维ＦＦＴ法更快，精度较高的光不检测技术。该技术只需采集一幅图象，不需要确定条纹级次，不存在“凹凸模糊”的问题。本文给出了一个典型试件的实验结果及分析。     

Quasi-equiripple approximation of minimum phase FIR filters by updating desired response

The authors present a numerical method for the Chebyshev approximation of minimum phase FIR digital filters. This method is based on solving a least squares (LS) problem iteratively. At each iteration, the desired response is transformed so as to have an equiripple magnitude error. This method makes it possible to design minimum phase FIR filters whose magnitude error is quasi-equiripple. Using this method, a quasi-equiripple solution is obtained very quickly. Since the proposed methods do not require any time-consuming optimisation procedure, they require less computational complexity than conventional methods. Finally, some examples to illustrate the advantage of the proposed methods are shown.     

Design of linear or minimum-phase fir filters by constrained chebyshev approximation

Constrained Chebyshev approximation is a known mathematical problem, and Remes' type algorithms for finding the solution have been described. It is shown in this paper that the classical Parks-McClellan program can be converted into a general program for constrained approximation. The program can serve for the design of both linear and minimum phase FIR digital filters.     

并行分布式算法FIR滤波器的FPGA实现

分布式算法(DA)是FPGA中实现FIR滤波器的重要手段。采用基本DA算法实现较高阶数的FIR滤波器时,占用的硬件资源较高,且随着变量的位数增加,其串行运算的特点也使其运行速度不高。为此,运用并行式的分布算法,将原LUT分解为若干较小LUT,并使参加运算的各变量各位组合同时送达查找表。QUARTUSⅡ仿真结果表明,滤波效果良好,资源消耗减少,运行速度显著提高。     

一维线性相位FIR数字滤波器的频域最小平方误差设计方法

本文提出了一种设计一维线性相位FIR数字滤波器的新方法。该方法采用频域的最小平方误差函数使所求的增益特性逼近所希望的增益特性 ,其计算公式非常简单 ,并可设计任意形状增益特性的FIR数字滤波器。设计实例表明提出的方法非常有效