Flat magnitude response FIR halfband low/high pass digital filters with narrow transition bands

MAXFLAT FIR low/high pass digital filters are traditionally designed to satisfy the constraints of maximal flatness at the ends of the frequency band. In this paper, we show that by moving the points of flatness to the inner band, halfband filters with narrow transition bands can be realized. This, however, affects the smoothness of their magnitude responses at the ends of the frequency band. We propose a new design of halfband filters having their points of flatness at the middle of the pass and stop bands. The resulting filters have significantly narrow transition bands as compared to the existing MAXFLAT designs, and yet their magnitude responses are quite smooth in the entire frequency band.     

A nearly optimum linear-phase digital FIR filters design

A new simple method to design linear-phase finite impulse response (FIR) digital filters, based on the steepest-descent optimization method, is presented in this paper. Starting from the specifications of the desired frequency response and a maximum approximation error a nearly optimum digital filter is obtained. Tests have shown that this method is alternative to other traditional ones such as Frequency Sampling and Parks–McClellan, mainly when other than brick wall frequency response is required as a desired frequency response.     

加权最小二乘法设计分数延迟FIR数字滤波器

用加权最小二乘法设计分数延迟FIR数字滤波器。在设计中,滤波器系数表示为分数延时量的多项式,对由多项式系数构成的矩阵进行行拉直,使之成为行向量以方便计算;用积分计算目标误差函数,相对于利用大量离散点值求和的方法,精度更高;求解拉直行向量时,采用矩阵三角分解,并合理调整计算顺序以避免病态计算。仿真计算表明,利用本文方法设计的分数延迟FIR数字滤波器的精度更高,复杂度更低。     

Laguerre discrete-time filter design

The design of discrete-time ideal filters by finite impulse response (FIR) method requires long FIR filter structures.This is due to the infinite impulse response characteristics of the ideal filters. Optimum Laguerre filter structures with smaller length can be used instead of FIR filters to reduce the order of the filters.In this paper the method of designing optimum Laguerre ideal low-pass, band-pass, high-pass, and band-reject filters is introduced. The optimization is performed by evaluating the Laguerre parameter and coefficients when the mean-square-error between the frequency response of the desired filter and its corresponding Laguerre network frequency response is minimum. The problem with the Laguerre filter design is the complexity of computations for evaluating the optimum Laguerre parameter. This complexity is reduced to one half by introducing a lemma.Both, analytical and numerical solutions are presented and the results are illustrated via some examples. The corresponding results yield a reduced filter order, and appropriate linear phase, with lower ripples in stop-band and pass-band compared to the conventional FIR filters.     

The design of multi-dimensional acoustic beamformers via window functions

The design of broadband beamformers can be formulated as a semi-infinite programming optimization problem, where the coefficients of the filters are determined such that the actual response of the microphone array is near a given desired response. This problem can be solved by existing optimization solvers after the discretization of the infinite constraints. However, this problem will become large-scale and it's expensive to find the optimal solution, as the discretization points grow and the filter length increases. In this paper, we propose a fast method based on the window functions. First, we formulate a simplified optimization problem to find the limit of the cost function values as the filter length is sufficiently long. Hence, the optimal frequency response vector is obtained and the corresponding filter coefficients can be calculated. Second, we apply the window method to truncate the limiting filter to obtain a finite FIR filters. The performance as well as the computational complexity are investigated to demonstrate the effectiveness and efficiency of the proposed method.     

Closed-form unbiased frequency estimation of a noisy sinusoid using notch filters

In this note, the problem of the frequency estimation of a sinusoid embedded in white noise is considered. The approach used herein is the minimization of the sample variance of the output of constrained notch filters fed by the noisy sinusoid. In particular, this note focuses on closed-form expressions of the frequency estimate, which can be obtained using notch filters having an all-zeros finite-impulse response (FIR) structure. The results presented in this note are as follows: 1) it is shown that the FIR notch filters obtained from standard second-order infinite-impulse response (IIR) filters are inadequate; 2) a new second-order IIR notch filter is proposed, which provides an unbiased estimate of the frequency; 3) the FIR filter obtained from the new IIR filter provides a closed-form unbiased frequency estimate; and 4) the closed-form frequency estimate obtained using the new FIR notch filter asymptotically converges toward the Pisarenko harmonic decomposition estimator and the Yule-Walker estimator.     

A New Design Approach for Nearly Linear Phase Stable IIR Filter using Fractional Derivative

In this paper,a new design method for digital infinite impulse response(IIR)filters with nearly linear-phase response is presented using fractional derivative constraints(FDCs).In the proposed method,design problem of an IIR frlter is constructed as the minimization of phase error between the desired and designed phase response of an allpass filter(APF)such that the designed lowpass filter(LPF)or highpass frlter(HPF)yields less passband(ep),and stopband errors(es)with optimal stopband attenuation(As).In order to have accurate passband(pb)response,FDCs are imposed on appropriate reference frequency,where the optimality of these FDCs are ensured by using a new greedy based sorting mechanism.The simulated results reflect the efficiency of the proposed method in term of improved passband response along with better transition width.However,small reduction in^is observed within the allowable limit,when compared to noin-fractional design approach,but the designed filter remains immune to wordlength(WL)effect.     

均匀线列阵时域宽带波束形成方法研究

时域宽带恒定束宽波束形成技术一般采用特殊频率响应的FIR滤波器组实现对不同频率的加权.对水下常用的均匀线列阵,利用切比雪夫方法设计了形成宽带恒定束宽波束的权值.通过对切比雪夫方法设计权值特性的分析,推导出实现加权的FIR滤波器组的相位响应关系式.根据推导结果得出设计的FlR滤波器组应为一组斜率不同的线性相位响应FIR滤波器.推导了滤波器组相位响应的计算公式.给出三种特殊频率响应FIR滤波器设计算法.通过仿真结果比较了三种方法设计的用于实现均匀线列阵恒定束宽加权的FIR滤波器组的性能.     

余弦调制子带滤波器组迭代设计的改进算法

余弦调制子带滤波器组的设计可以转化成一个高维非线性优化问题,传统迭代设计方法虽然避免了复杂的直接求解过程,但是其混叠误差的抑制依赖于滤波器阻带衰减的大小,设计出的滤波器往往阶数过高。本文提出了一种改进的子带余弦调制滤波器组迭代设计算法,其代价函数除了包括子带系统响应和子带滤波器阻带能量之外,还添加了系统一次混叠项因子,因此更好地抑制了混叠误差。本文将新的代价函数表示成滤波器系数的二次函数形式,并推导出其极值点的闭合解表达式。算法保留了传统迭代方法逐渐逼近极值点的思想,简单易于实现。仿真结果表明与传统迭代设计方法相比,本文算法获得的子带滤波器组具有更小的混叠误差和更低的滤波器阶数。     

Design of nearly perfect reconstructed non-uniform filter bank by constrained equiripple FIR technique

In this paper, an efficient iterative algorithm is proposed for the design of multi-channel nearly perfect reconstructed non-uniform filter bank. The method employs the constrained equiripple FIR technique to design the prototype filter for filter banks with novelty of exploiting a new perfect reconstruction condition of the non-uniform filter banks instead of using complex objective functions. In the proposed algorithm, passband edge frequency (ω_p) is optimized using linear optimization technique such that the filter coefficients values at quadrature frequency are approximately equal to 0.707. Several design examples are included to illustrate the efficacy of this methodology for designing non-uniform filter bank (NUFB). It was found that the proposed methodology performs better as compared to earlier reported results in terms of reconstruction error (RE), number of iteration (NOI) and computation time (CPU time). The proposed algorithm is very simple, linear in nature, and easy to implement.     

基于支持向量机的滤波器设计与硬件实现

针对传统有限脉冲响应(FIR)滤波器设计方法和神经网络设计方法的不足,在改进使用支持向量机(SVM)设计FIR滤波器方法的基础上,提出了SVM设计FIR滤波器的硬件实现方法.使用理想滤波器的幅值响应训练SVM,得到训练参数,据此构建基于SVM的FIR滤波器的嵌入式系统.软件实现FIR滤波器的训练部分,硬件实现FIR滤波器的测试部分.单次判定测试向量的时间约为3500 ns,滤波准确率可达到98.41%.设计的滤波器具有良好的幅频特性,边界控制精确,逼近理想滤波器.     

基于变学习率三角基函数神经网络的4型FIR滤波器设计

本文提出一种基于变学习率三角基函数神经网络的线性相位4型FIR滤波器设计方法。该方法根据三角基函数神经网络与线性相位4型FIR滤波器幅频特性之间的关系,构建了一种变学习率三角基函数神经网络模型,在神经网络训练过程中引入变学习率算法自调整学习率取值,解决学习率通常依靠经验或试凑法确定带来的不确定性,提高神经网络的学习效率和收敛速度。通过训练神经网络的权值,使设计的FIR滤波器幅频响应与理想幅频响应在整个通带和阻带内的误差平方和最小。文中利用该方法对FIR高通滤波器和带通滤波器进行了优化设计,仿真结果表明了该方法设计FIR滤波器的有效性和优越性。     

An alternative FIR filter for state estimation in discrete-time systems

To overcome the resulting problems of existing finite impulse response (FIR) structure filters, this paper proposes an alternative FIR filter for state estimation in discrete-time systems, which is derived from the well-known Kalman filter with recursive infinite impulse response (IIR) structure. The proposed FIR filter obtains a posteriori knowledge about the window initial condition from the most recent finite observations, while existing FIR filters handle this task arbitrarily or heuristically. The gain matrix for the proposed FIR filter incorporates a posteriori knowledge about the window initial condition during its design and is shown to be time-invariant. The proposed FIR filter is shown to have good inherent properties such as unbiasedness and deadbeat. Through extensive computer simulations, the proposed FIR filter can be shown to be comparable with the Kalman filter for the nominal system and better than that for the temporarily uncertain system.     

复系数FIR数字滤波器的神经网络设计方法

神经网络是一种设计实系数FIR滤波器的有效算法,为了将该方法扩展到复数域,建立统一的基于神经网络的滤波器设计框架,文中提出了一种用多层神经网络设计任意幅频响应的复系数FIR数字滤波器的新算法,主要思想是将设计问题转化为实系数多层神经网络的训练问题,在实数域对幅频响应的平方误差函数的实部和虚部分别进行最小化,误差将收敛到全局最小点.实验结果表明,利用该算法设计的滤波器具有较小的幅频响应误差和群延迟误差.该算法能解决具有任意幅频响应和群延迟要求的问题,是一种有效的设计算法.     

一种水下机器人传感器故障诊断与容错控制方法

采用自适应滤波器ＦＩＲ 对水下机器人进行在线自适应建模,并利用ＬＭＳ算法来调节滤波器的权系数．通过对滤波器权系数和误差信号平方的分析,实时检测出传感器的故障,并应用ＦＩＲ 滤波器输出替代故障传感器信号,实现传感器故障情形下水下机器人容错控制．应用该方法对Ｏｕｔｌａｎｄ１０００水下机器人传感器的故障进行检测和容错,实验结果表明所提故障检测方法准确可靠,具有较好的容错效果．     

Power and delay efficient fir filter design using ESSA and VL-CSKA based booth multiplier

FIR filter plays a major role in digital image processing applications. The power and delay performance of any FIR filter depends on the switching activities between the filter coefficients (FCs) and its basic arithmetic operations (i.e., multiplication and addition) performed in the convolution equations. In this paper, a new FIR filter is designed using Enhanced Squirrel Search Algorithm (ESSA) and Variable latency Carry skip adder (VL-CSKA) based booth multiplier. The proposed ESSA algorithm selects an optimal FC by minimizing the switching activities of FC based on the ripple contents, power and Transition width parameter to meet the required specifications of FIR filter in the frequency domain. Also, the VL-CSKA based booth multiplier is proposed to reduce the delay of FIR filter with parallel addition of partial products (PPs). In this design, the VL-CSKA adders utilize variable size and compound gate-based skip logic to deduce the delay with low power. The proposed FIR filter is simulated in Xilinx working platform by developing Verilog coding. The simulation result shows that the proposed FIR filter outperforms the state-of-the-art FIR filters by consuming only 0.142 mW power with delay of 28.175 ns.     

Identification of sparse impulse responses – design and implementation using the partial Haar block wavelet transform

This paper proposes an implementation for identifying sparse impulse responses. The new scheme follows the approach in which the location of the channel response peak is estimated in the wavelet domain. A short time-domain adaptive filter is then located about the estimated peak to identify the sparse response. The primary purpose of this paper is to present an efficient design of such a system. The use of a new block wavelet transform results in up to 70% less computational complexity and improved peak detection, as compared to previous solutions. A new robust time-domain adaptive filtering location and update scheme is also proposed that significantly reduces the occurrence of jitter problems and leads to improved residual mean-square error performance. The behavior of the transform-domain adaptive filter is analyzed, the Wiener solution is determined, and an accurate analytical model is obtained for the mean-square deviation of the adaptive coefficients. Monte Carlo simulations show excellent echo cancellation performance for typical ITU-T echo channels.     

Hardware based genetic evolution of self-adaptive arbitrary response FIR filters

This work presents a hardware implementation of an FIR filter that is self-adaptive; that responds to arbitrary frequency response landscapes; that has built-in coefficient error tolerance capabilities; and that has a minimal adaptation latency. This hardware design is based on a heuristic genetic algorithm. Experimental results show that the proposed design is more efficient than non-evolutionary designs even for arbitrary response filters. As a byproduct, the paper also presents a novel flow for the complete hardware design of what is termed as an Evolutionary System on Chip (ESoC). With the inclusion of an evolutionary process, the ESoC is a new paradigm in modern System on Chip (SoC) designs. The ESoC methodology could be a very useful structured FPGA/ASIC implementation alternative in many practical applications of FIR filters.     

Taylor series expansion based repetitive controllers for power converters,subject to fractional delays

Digital repetitive controllers are widely employed to track/reject the periodic signals with zero steady-state error. Their implementation involves the use of single or multiple digital delay elements. Practically, the delay element is implemented by the use of memory locations, where samples are held and released after a specific number of sampling periods, equivalent to the desired time delay. A problem arises when the desired time delay becomes a non-integer multiple of the sampling time. Such time delays can be accurately realized by employing a fractional delay filterThis paper presents a Taylor Series expansion based digital repetitive controller designed to implement any (integer, non-integer) delay in the control of power converters, occurring due to uncontrollable variations in the reference frequency. The T3644aylor Series expansion transforms the fractional delay filter design problem to a differentiator/sub-filter design. Finite impulse response (FIR) and infinite impulse response (IIR) fractional delay (FD) filter concepts can be applied to realize the required fractional delay. This structure provides efficient on-line tuning capabilities i.e. FD can easily generate any required fractional delay without redesigning the filter when the delay parameter varies. An example is demonstrated to show the effectiveness of this approach, for a single-phase power inverter feeding a passive load.