A new closed form method for design of variable bandwidth linear phase FIR filter using Bernstein multiwavelets

In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response filters using Bernstein polynomial Multiwavelets is proposed. In this method, approximation has been achieved by linearly combining the fixed coefficient linear phase filters with Bernstein multiwavelets, which are used to tune bandwidth of the filter. Optimisation has been achieved by minimising the mean square error between the desired and actual filter response which leads to a system of linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, which reduces the computational complexity. The simulation results illustrate significant improvement in errors in passband (e_p), and stopband (e_s) as compared to earlier published work.     

High performance continuous variable bandwidth digital filter design for hearing aid application

A low complexity, low delay reconfigurable digital filter structure for hearing aids is proposed in this paper. The main objective is to match a given human audiogram, with minimum error. The high computational complexity in the conventional uniform and non-uniform filter bank techniques, probes to shift the design paradigm towards variable filter structure. In this paper, Farrow structure based design is used to realize an arbitrary sample rate converter, making use of a differentiator based model, by which the bandwidth can be continuously varied. The proposed design also considers the importance of the power, area, and” delay in such a critical scenario. Exhaustive comparisons are performed with the existing literature on audiogram matching, and our design is very competitive when compared to the designs in the literature, not only with respect to the matching error but also with respect to area, power dissipation, and hardware complexity.     

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.     

一种二阶锥规划通带线性相位FIR滤波器的设计

在有限冲激响应（Finite Impulse Response,FIR）滤波器设计中,如果系统只要求通带或某个频域区间具有线性相位而其他频域区间相位非线性,则系数对称的FIR滤波器设计方法不再适用。为此,提出了一种基于二阶锥规划（Second-Order Cone Programming,SOCP）的通带线性相位FIR滤波器设计方法。该方法使用二阶锥规划实现滤波器设计,其中优化目标为通带最小群延迟,约束条件为全频域振幅误差。实验结果显示,所提方法设计的FIR滤波器有着很好的幅频特性和通带线性相位,通带群延迟误差很小。该方法实现简单,计算复杂度低,可以广泛应用于数字信号处理领域。     

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.     

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.     

一种基于FPGA节省资源实现FIR滤波器的设计方法

有限长脉冲响应（FIR）滤波器的结构决定了用现场可编程门阵列（FPGA）设计非常消耗触发器资源或存储器资源。以n阶滤波器为例,提出一种节省触发器和双口RAM的读写操作方法。通信系统应用仿真表明,与常规FIR滤波相比较,本文方法不仅滤波效果良好,而且大量减少乘法器和加法器数量,有效节省触发器和双口RAM。滤波器阶数越高,越节省资源。     

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 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.     

一种利用曲线拟合设计内插滤波器的新方法

与传统的从频域来设计内插滤波器的方法不同，本文从滤波器脉冲响应的方向入手，提出了一种利用曲线拟合设计性能较高的内插滤波器的新方法，从而克服了传统方法利用穷搜索寻找最佳系数花费时间过长的缺点。这种方法尤其适用于内插滤波器系数较多或者需要的精度较高的情况。     

基于传输零点的广义切比雪夫型LC滤波器快速设计法

通过对不同结构的广义切比雪夫型LC滤波器的传输零点特性进行分析验证,得到适用于N阶广义切比雪夫型LC滤波器传输零点特性的结论。基于这些结论提出一种快速设计广义切比雪夫型LC滤波器的方法,大大缩短了设计滤波器的时间。并且该方法可以在实现滤波器带外截止特性的同时,实现滤波器小型化,在科学研究和工程应用中具有重要意义。     

A Survey of FIR Filter Design Techniques: Low-complexity,Narrow Transition-band and Variable Bandwidth

In the present century, digital signal processing (DSP) approaches are considered to be one of the most powerful technologies which may shape the science and technology in coming decades. From 1970 onwards, a drastic revolution took place in a wider domain of DSP which has made it popular in several studies such as radar and sonar signal processing, digital televisions, wireless communication scenarios and other multimedia setup etc. Digital filters form the backbone of this DSP architecture and in point of fact the field of digital filter design has drawn justified recognition from the researchers throughout the world for the last 50 years. In connection to this, thousands of research articles may be found from the literature which had extensively addressed on the design of such filters. In order to meet the requirement of narrow transition-band, finite impulse response (FIR) filters are commonly assumed to be of higher order and accordingly it significantly enhances computational complexity. In regard to this, construction of hardware efficient digital filters had drawn significant consideration which aims to include minimum hardware elements during its application and consequently consumes less power. This review paper illustrates various techniques for the implementation of hardware efficient narrow transition-band FIR filter and investigates a number of favourable attributes which are capable in sustaining the stringent requirements of communication standards. A good number of relevant articles are taken from the literature so as to make a robust and complete review.     

A new method for adaptive IIR filter design based on tabu search algorithm

Adaptive digital filters have proven their worth in a wide range of applications such as channel equalisation, noise reduction, echo cancelling, and system identification. These filters can be broadly classified into two groups: finite impulse–response (FIR) and infinite impulse–response (IIR) filters. IIR filters have become the target of increasing interest because these filters can reduce the filter order significantly as compared to FIR filters. Tabu search is a heuristic optimisation algorithm which has been originally developed for combinatorial optimisation problems. It simulates the general rules of intelligent problem solving and has the ability of discovering the global minima in a multi-modal search space. In this work, a novel method based on tabu search is described for the design of adaptive IIR filters.     

A new design method of CDMA spreading codes based on multi-rate unitary filter bank

It is well-known that the multi-valued CDMA spreading codes can be designed by means of a pair of mirror multi-rate filter banks based on some optimizing criterion. This paper indicates that there exists a theoretical bound in the performance of its circulating correlation property, which is given by an explicit expression. Based on this analysis, a criterion of maximizing entropy is proposed to design such codes. Computer simulation result suggests that the resulted codes outperform the conventional binary balanced Gold codes for an asynchronous CDMA system.     

A new hybrid wavelet-Kalman filter method for the estimation of dynamic system

A new hybrid wavelet-Kalman filter method for the estimation of dynamic system is developed, Using this method, the real-time multiscale estimation of the dynamic system is implemented, and the observation equation established is for the object signal itself rather than its wavelet decomposition. The simulation results show that this method can be used to estimate the object＇s state of the stacked system, which is the foundation of multiscale data fusion; besides the performance of the new algorithm developed in the letter is almost optimal.     

A fast perturbation method for the design of linear phase fir digital filters of finite wordlength using single-frequency filters

In this paper a fast perturbation algorithm for the design of linear phase FIR digital filters of finite wordlength is presented. The original set of filter coefficients are obtained using the Parks-McClellan algorithm, then a small perturbation is given to these sets of coefficients. The peak deviations corresponding to the rounded set of coefficients obtained from the original and the perturbed sets are compared and the set of coefficients with the lower value of peak deviation is stored as the best set of coefficients. A further perturbation is given to the infinite precision coefficents and these are rounded to the required wordlength. Comparison is made between these rounded sets and the present best set with respect to peak deviation and the better set is stored as the best set of coefficients. This process is repeated for a finite number of times or until the peak deviation is sufficiently low. To obtain the compensating filter coefficients single-frequency filters are used. Mathematical justification for the single-frequency design is given. Important results for a large number of design examples are presented to illustrate the speed and effectiveness of the algorithm.     

多路光信号功率分配与设计新方法

提出了一种基于规格型光二分路器的多路光功率分配方法,将多路分光比的设计及其分路器的制作转化为用各种规格型号的光二分路器的组合实现多路光功率的合理分配.给出了一种新的光二分路器规格表,并通过具体实例详细介绍了这种多路光功率分配的方法和过程.事实证明,该方法具有简单、易行、网络成本造价低、利于网络器件的备用和维修的优点.     

A new prognostics method for state of health estimation of lithium-ion batteries based on a mixture of Gaussian process models and particle filter

State of health (SOH) estimation for batteries is a key component in the prognostics and health management (PHM) of battery driven systems. Due to the complicated operating conditions, it is necessary to implement the prognostics under uncertain situations. In this paper, a novel integrated approach based on a mixture of Gaussian process (MGP) model and particle filtering (PF) is presented for lithium-ion battery SOH estimation under uncertain conditions. Instead of directly assuming a certain state space model for capacity degradation, in this paper, the distribution of the degradation process is learnt from the inputs based on the available capacity monitoring data. To capture the time-varying degradation behavior, the proposed method fuses the training data from different battery conditions as the multiple inputs for the distribution learning using the MGP model. Then, a recursive updating of the distribution parameters is conducted. By exploiting the distribution information of the degradation model parameters, the PF can be implemented to predict the battery SOH. Experiments and comparison analysis are provided to demonstrate the efficiency of the proposed approach.