On the coefficient quantization of Multiplicative FIR filters

This paper analyzes the effects of coefficient quantization of Multiplicative Finite Impulse Response (MFIR) filters used to approximate the behavior of pole filters. Statistical analysis, zero displacement sensitivity and frequency domain analysis are used as measures of the filter performance for different coefficient lengths. A practical expression for determining the required number of bits for the coefficient quantization as a function of a predefined maximum deviation in the magnitude response is proposed in combination with an alternative method based on a time domain analysis. The time domain analysis allows, for a specific pole approximation, to investigate the sensitivity of the MFIR structure to coefficient variations. The paper concludes that, statistically, the MFIR pole approximation filter does not require a larger number of quantization bits for its coefficients than the corresponding Infinite Impulse Response (IIR) filter.     

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.     

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.     

数字下变频中的FPGA高效滤波器设计

介绍了一种在FPGA上实现高效窄带有限冲击响应滤波器(FIR)的设计方法.该方法利用数字下变频抗混叠滤波器的多速率和窄带的特点,采用插值FIR滤波器(IFIR)和多相滤波器相结合的设计思路,实现了该滤波器的高效设计.     

基于RAG-n算法的低成本FIR滤波器实现

基于FIR数字滤波器多常数乘法的图表示法,利用MATLAB对RAG-n算法进行了实现。通过仿真该算法在大多数情况下都可以高效地解决加法器优化问题,有效降低了FIR滤波器常系数乘法的复杂度。在FPGA上用Verilog HDL语言对优化实例进行了实现,其综合结果表明,该方法可以有效减少逻辑单元的消耗,适用于低成本数字系统设计。     

解离散系数滤波器设计问题的分支定界算法

基于离散系数滤波器设计问题已有的半定规划松弛模型,利用文献[6]的方法给出了该问题的二次规划松弛模型,该模型能给出比半定规划模型更好的界,然后运用分支定界方法求解该模型。与随机扰动方法相比,该方法能得到一个性能更好的次优解,对于精度要求较高的滤波器设计问题,这种方法非常有效,并通过了仿真实验的证实。     

Optimal horizons for a one-parameter family of unbiased FIR filters

In this paper, we find the optimal horizons and sampling intervals, both in the sense of the minimum mean square error (MSE), for a one-parameter family of the discrete-time unbiased finite impulse response (FIR) filters. On a horizon of N_l points in the nearest past, the FIR and the model k-state are represented with the l-degree and m-degree polynomials, respectively. The noise-free state space model is observed in the presence of zero-mean noise of an arbitrary distribution and covariance. The approach is based on the following. The FIR filter produces an unbiased estimate if lm. In order to reduce the noise, N_l needs to be increased. The model fits the increased horizon with a higher degree polynomial, m>l. Minimization of the mean square error for m>l gives the optimal horizon and sampling interval. Justification is provided for the global positioning system (GPS)-based measurements of the first state of a local crystal clock provided in the presence of uniformly distributed sawtooth noise induced by the GPS timing receiver.     

Image denoising using 2-D FIR filters designed with DEPSO

Digital images are often corrupted by additive noises during transmission. Thus, how to alleviate noise as much as possible has received concerns for decades. In this paper, we present a simple denoising method based on two dimensional (2-D) finite impulse response (FIR) filtering, where by differential evolution particle swarm optimization (DEPSO) algorithm, five two dimensional finite impulse response filters are designed to filter different kinds of pixels. Comprised by differential evolution algorithm and particle swarm optimization algorithm, differential evolution particle swarm optimization algorithm is effective and robust, which helps to yield better denoise performance. And computer simulation demonstrates that the proposed method is superior to the conventional lowpass filtering method, as well as the modern bilateral filtering and stochastic denoising method.     

FIR filters and recursive forms for continuous time-invariant state-space models

An FIR (finite impulse response) filter and an FIR smoother are introduced for continuous time-invariant state-space models. It is shown in this note that finite impulse responses of the FIR filter and smoother can be easily determined by solving a simple Riccati-type matrix differential equation on a finite interval. Especially for systems with stationary processes, finite impulse responses of the FIR filter and smoother become time-invariant and can be computed from simpler equations. For fast computational purposes, recursive forms of the FIR filter and smoother are derived by using adjoint variables. In this case all gains for recursive forms are shown to be constant.     

基于子项空间技术的低复杂度FIR滤波器实现

基于子项空间共享技术,利用硬件描述语言编程,在FPGA上对FIR数字滤波器进行了实现。该设计将常系数乘法模块用加法和移位操作来实现,并利用子项共享有效地减少加法器个数。综合结果表明,所提方法可以有效节省硬件资源,降低实现成本,适用于低功耗数字系统设计。     

FIR filters for online trajectory planning with time- and frequency-domain specifications

In this paper, the use of FIR (Finite Impulse Response) filters for planning minimum-time trajectories for robots or automatic machines under constraints of velocity, acceleration, etc. is presented and discussed. In particular, the relationship between multi-segment polynomial trajectories, i.e. trajectories composed of several polynomial segments, each one possibly characterized by constraints on one or more specific derivatives (i.e. velocity, acceleration, jerk, etc.), and FIR filters disposed in a cascade configuration is demonstrated and exploited in order to design a digital filter for online trajectory planning. The connection between analytic functions and dynamic filters allows a generalization of these trajectories, usually obtained by second- or third-order polynomial functions (e.g. trapezoidal velocity and double S velocity trajectories), to a generic order with only a modest increase of the complexity. As a matter of fact, the computation of trajectories with higher degree of continuity simply requires additional FIR filters in the chain. Moreover, the modular structure of the planner provides a direct frequency characterization of the motion law. In this way, it is possible to define the trajectories by considering constraints expressed in the frequency-domain besides the classical time-domain specifications, such as bounds on velocity, acceleration, and so on. Two examples illustrate the main features of the proposed trajectory planner, in particular with respect to the problems of multi-point trajectories generation and residual vibrations suppression.     

基于混沌粒子群优化算法的FIR数字滤波器设计

有限脉冲响应(FIR)数字滤波器的设计,实质上是一个多参数优化问题.将粒子群优化算法与混沌相结合来设计FIR数字滤波器,并用该方法设计了一个高通滤波器.与用Parks-McClellan算法设计得到的高通滤波器进行对比发现,基于混沌粒子群优化算法(CPSO)的FIR滤波器通带波动小,阻带衰减大,从而证明了该算法的有效性和优越性.     

Eigenfilter design of linear-phase FIR digital filters using neural minor component analysis

This paper proposes a minor component analysis-based neural learning algorithm for designing linear-phase finite impulse response digital filters. The objective function to be minimized in the least-squares design can be formulated as the eigenvalue problem for solving an appropriate real, symmetric, and positive-definite matrix. To achieve the eigenfilter design, an alternative neural learning rule based on the minor component analysis algorithm is exploited. The optimal filter coefficients corresponding to the eigenvector of the smallest eigenvalue of the positive-definite matrix can be achieved in an iterative manner, avoiding the complex computation of eigenvalue decomposition. Furthermore, the learning step parameter that affects the convergence performance is investigated empirically. The simulation results indicate that the proposed neural-based approach can be applied to eigenfilter design and yields a lower computational complexity compared with traditional matrix algebraic-based approaches.     

Optimal design of FIR linear phase digital filters via convex quadratic programming method

Many methods exist for designing FIR linear phase digital filters by using various optimization techniques. An optimization design method via the convex quadratic programming method is investigated in this paper. The aim of this method is to design digital filters with certain desired frequency responses that keep the passband ripple to a minimum while maintaining a balance between opposite characteristics of frequency responses, i.e. the narrow transition band and the great stopband attenuation. In order to verify the effectiveness of this method, low-pass filters are designed and comparison studies with other typical optimization methods are given.     

A class of low-pass FIR input shaping filters achieving exact residual vibration cancelation

This paper describes the construction of low-pass FIR filters for application as command input shapers in motion control systems. The filters are designed to operate on an arbitrary command input signal to ensure a finite settling time for system modes with known natural frequency and damping ratio. In addition, the required roll-off rate of the filter frequency response may be prescribed in the design. Excitation of unmodeled high-frequency modes can thereby be reduced. The filters also produce an input-smoothing effect that is useful in situations where discontinuities in the input signal or its derivatives would be detrimental to system performance or function. Numerical case studies are presented to clarify these effects.     

Design of nonrecursive FIR filters with simultaneously MAXFLAT magnitude and prescribed cutoff frequency

Maximally-flat (MAXFLAT) FIR filter design still has a problem in overcoming the cutoff-frequency error due to approximation of the desired frequency response by some closed-form solution. In order to overcome such a difficulty, this paper describes a new method for the design of nonrecursive FIR filters with simultaneously MAXFLAT magnitude and accurate cutoff frequency. The proposed method provides a general formula to find interpolation coefficients for a new closed-form expression of this filter type, obtained by solving solutions of linear differential equations that are derived from the maximal flatness and cutoff-frequency conditions. In addition, this method efficiently determines the optimal degree of flatness by using a powerful objective error function derived from this closed-form solution, and allows direct and simple computation of the coefficients of the filter with the desired frequency response. The design examples are shown to provide a complete and accurate solution for the design of such filters.     

Receding-horizon unbiased FIR filters for continuous-timestate-space models without a priori initial state information

A receding horizon unbiased finite-impulse response filter (RHUFF) is proposed for continuous-time state space models. Linearity, unbiasedness, finite-impulse response (FIR) structure, and independence of the initial state information will be required in advance, in addition to a performance index of minimum variance. The proposed RHUFF is obtained by directly minimizing the performance index with the unbiasedness constraint. The proposed RHUFF is represented first in a standard FIR form and then in an iterative form. It is shown that the RHUFF is equivalent to the existing receding horizon (RH) Kalman FIR filter. The former is more systematic and logical, while the latter is heuristic due to the handling of infinite covariance of the initial state information     

带残余补偿的外推冲激响应低成本FIR滤波器实现

基于带残余补偿的外推冲激响应设计技术,利用硬件描述语言编程在集成电路上对FIR数字滤波器进行了综合.该技术利用冲激响应的准周期特性近似滤波器系数,有效降低了FIR滤波器常系数乘法的复杂度,并通过残余补偿降低滤波器阶数,同时应用子项共享技术进一步减少加法器个数.综合结果表明所提方法可以有效节省高阶FIR滤波器硬件资源的消耗,适用于低成本数字系统设计.