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.     

设计有限字长FIR数字滤波器的Tabu优化算法

该文提出了设计有限字长FIR数字滤波器的Tabu优化算法,这是一种模拟人的记忆过程的并行优化算法。首先,详细描述了Tabu算法并给出了计算步骤;然后将Tabu算法应用于有限字长FIR数字滤波器的优化设计;最后给出了模拟计算结果。     

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.     

用DSP实现FIR数字滤波器

FIR滤波器具有幅度特性可随意设计、线性相位特性可严格精确保证等优点,因此在要求相位线性信道的现代电子系统,如图像处理、数据传输等波形传递系统中,具有很大吸引力。本文简单介绍了其线性相位条件和设计方法,并且提供了一种用DSP实现的方法。     

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.     

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.     

An iterative approach for minimax design of multidimensional quadrature mirror filters

In this paper, a nest of iterative techniques is proposed for the minimax design of quadrature mirror filter (QMF) banks. The method can be generalized such that multidimensional QMF banks can be designed by the proposed algorithm. For a given weighting function, an iterative method is used to minimize the objective error function in the inner iterations. To further reduce the peak error of overall magnitude response, an iterative weighting-updated technique is adopted in the outer iterations. Comparing with the existing works concern the design of perfect-reconstruction QMF banks, only one of the filters is needed to be designed under the cost of magnitude distortion, but the system complexity can be reduced drastically. Several examples, including design of 2-D and 3-D QMF banks, will be presented to demonstrate the effectiveness of the proposed method.     

Design of smallest size two-dimensional linear-phase FIR filters with magnitude error constraint

This paper presents an online procedure that produces the smallest feasible size of two-dimensional FIR filters with prescribed magnitude error constraint. The procedure uses the mean square normalized error of constrained and unconstrained least-square filters to produce the initial and the subsequent sizes that converge to the smallest feasible one in a few iterations, where the constrained least-square filters are defined as the least-square filters satisfying the magnitude error constraint. The procedure finally returns a smallest size filter that satisfies the magnitude error constraint and has least total squared magnitude error. Design examples of diamond-shaped, rectangular, and elliptic filters are provided, and comparisons with an exhaustive search are given.     

A Fast FIR filtering technique for multirate filters

This paper presents a technique for applying Fast FIR Algorithms (FFAs) to interpolation and decimation filters. In the event that the prototype filter has a symmetric impulse response, it is shown that the subfilters which result from the application of the FFA will be jointly symmetric. This fact may be exploited in order to further reduce the computational complexity of the system. The effect of transposition upon the proposed structure is discussed, and it is shown that transposition yields a more economical structure in the case of a decimation filter. The computational complexity of the proposed schemes is shown to compare favorably with that of the standard parallel filtering approach.     

An improved design method based on polyphase components for digital FIR filters

This paper presents an efficient design of digital finite impulse response (FIR) filter, based on polyphase components and swarm optimisation techniques (SOTs). For this purpose, the design problem is formulated as mean square error between the actual response and ideal response in frequency domain using polyphase components of a prototype filter. To achieve more precise frequency response at some specified frequency, fractional derivative constraints (FDCs) have been applied, and optimal FDCs are computed using SOTs such as cuckoo search and modified cuckoo search algorithms. A comparative study of well-proved swarm optimisation, called particle swarm optimisation and artificial bee colony algorithm is made. The excellence of proposed method is evaluated using several important attributes of a filter. Comparative study evidences the excellence of proposed method for effective design of FIR filter.     

分数阶数字FIR微分器的快速WSLD设计算法

一阶逼近格林瓦尔-莱特尼科夫(G-L)加权系数的计算具有准确快速的递推公式,而高阶逼近鲁比希加权系数的求解则复杂度高,计算消耗时间长。本文通过傅里叶变换证明了鲁比希算子的逼近阶,并基于移位鲁比希算子提出一类四阶逼近的加权移位鲁比希差分(WSLD)算子。从数字信号处理角度分析WSLD算子滤波特性,设计基于WSLD算子的分数阶数字FIR微分滤波器并进行数值仿真验证。对比Al-Alaoui、鲁比希2种典型分数阶算子,结果表明,利用WSLD算子求解分数阶数字FIR滤波器滤波系数的算法简单、高效,且相对其他算子能有效减小吉布斯效应影响。     

Minimum-phase fir precoder design for multicasting over MIMO frequency-selective channels

To maximize the throughput of frequency-selective multicast channel, the minimum-phase Finite Impulse Response (FIR) precoder design is investigated in this paper. This problem can be solved in two steps. Firstly, we focus on designing a nonminimum-phase FIR precoder under the criterion of maximizing the throughput, and develop two efficient algorithms for the FIR precoder design from perspectives of frequency domain and time domain. In the second step, based on the theory of spectral factorization, the nonminimum-phase FIR precoder is transformed into the corresponding minimum-phase FIR precoder by a classic iterative algorithm without affecting the throughput. Numerical results indicate that the achievable rate of the proposed design has remarkable improvement over that of existing schemes, moreover, the group delay introduced by the FIR precoder is minimized.     

Design of FIR filter ISOTA with the aid of genetic algorithm

The field of digital signal processing has been receiving justified attention over the years because of a number of reasons including sophisticated algorithms, high computational speed and wider area of applications. In connection to this, design of finite impulse response (FIR) filter has drawn the attention of researchers throughout the globe. A number of promising developments has been carried out over the last few decades which emphasize on the design of hardware efficient filter structure. In this paper, a new technique of FIR filter design has been addressed by virtue of genetic algorithm. Filter coefficients have been searched over the discrete space in such a way that the architecture consists of shifts and only two adders. As a matter of fact, the proposed FIR filter involving shift and only two additions (ISOTA) results in minimal hardware cost during its implementation. This has been illustrated by means of a few example filters in this work. Some of the recently proposed FIR ISOTA filters have also been taken for the purpose of comparison. Finally, the proposed filter has been implemented on Altera Cyclone IV FPGA board.     

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。     

Two-dimensional digital filters for geophysical applications: A simple design method leading to an easy implementation

A simple procedure for the design of two-dimensional digital filters will be presented. Its main interest is in the field of geophysical signal processing, since the design implies in these cases simple structures for the implementation. The 2-D problem is reduced to one, two or complicated cases to several 1-D problems. By 3 examples, relevant in geophysics, the power of this method will be demonstrated. The design is applicable for arbitrary ideal frequency responses, however the simple realization will be lost in general. The result is a suboptimal filter, which can be used, if desired, as an initial solution for an L_∞-approximation. However, the efficiency of the presented method is established by the fact that the design and implementation go hand in hand and are adapted to the special problem under consideration.     

一种改进的星载SAR俯仰向DBF处理技术

在星载SAR系统的高分辨率宽测绘带成像应用中,为了增大接收增益,提高回波的信噪比,可利用数字波束形成(DBF)技术实现俯仰向多通道接收并处理回波信号。该文分析并推导出了俯仰向通道的响应函数。基于这一结果,提出了一种时变加权与FIR滤波相结合的DBF处理方法,并且给出了系统实现框图。与其它DBF方法相比,该方法能在不增加系统实现复杂度的前提下,实现对长脉冲的接收增益最大化与系统性能最优化。仿真结果表明,该方法能够近似达到理论上的系统性能最优值。     

基于全相位陷波器解析设计的啸叫去除

为了快速且精准地抑制助听器中的啸叫效应,该文提出一种中心频率可以精确控制的全相位有限脉冲响应(FIR)陷波器解析设计。首先,为了获得较高的陷波精度,引入了整数部分m和小数部分λ来控制陷波的中心频率。然后,设计了一个偶对称的闭式解析式来计算陷波器系数。最后,为了保证输出信号的连续性和线性相位,进行数据延拓和截取操作。该陷波器具有线性传输特性,避免了非线性失真。为了检验陷波器的滤波性能,将其应用在助听器中去除啸叫。实验结果表明,该滤波器在啸叫频率下的衰减值可达–330 dB,信噪比达22 dB,输出波形质量好,算法复杂度低,鲁棒性高,具有一定的应用前景。     

FPGA realization of FIR filters for high-speed and medium-speed by using modified distributed arithmetic architectures

This paper presents the design optimization of fully pipelined architectures for area-time-power-efficient implementation of finite impulse response (FIR) filter. The architectures are designed to obtain a suitable area-time tradeoff. Analysis of the performance of different filter orders and different address lengths of partial tables indicate the choice of four input partial tables presents the best of area-time-power-efficient realizations of FIR filter compared with the existing LUT-less DA-based implementations of FIR filters in both high-speed and medium-speed. Moreover, a number of further experiments not only shows the pipeline register’s significant influence to the maximum frequency of the FIR filters but also indicates it also has area usage. Final experiment shows that with the help of using pipeline register, the choice of 4-bits-per-clock (4BPC) of the architecture for word-length N=8 with four input partial table yields the best cost-effective when comparing with other different cases in both high-speed and medium-speed implementations.     

数字滤波器的近似等波纹设计法

本文证明了数字滤波器的自适应设计法等价于MMSE设计法，并提出用幅度误差函数对代价函数进行自适应迭代的算法达到近似等滤纹数字滤波器的自适应设计法．实验证明该设计方法简单有效，适合用于滤波器的工程设计。     

Design of optimal digital lattice filter structures based on genetic algorithm

In this paper, a new class of lattice-based digital filter structures is derived. The optimum structure problem is formulated in terms of minimizing the signal power ratio with respect to the two sets of free parameters in the proposed structures. An efficient genetic algorithm is proposed to solve the optimum structure problem with the constraint on the structure parameters to be represented in signed power-of-two format. Two design examples are given, in which the optimized structures show excellent finite wordlength properties such as very low parameter sensitivity and very uniform signal powers across signal nodes and outperform the classical lattice structures.