Complex coefficient fir digital filters

The complex FIR digital filter is a filter that has complex coefficients in itsZ-domain transfer function. The set of coefficients is determined, based on some criterion, to meet predefined requirements. On this basis, an algorithm is proposed for designing FIR digital filters with asymmetric amplitude response in conjunction with linear phase. Minimax approximation has been adopted for determining the set of coefficients, where the associated set of overdetermined linear equations is solved by using an efficient linear programming algorithm. Computer simulations show that, to meet prescribed specifications, the proposed design algorithm yields a complex FIR digital filter with the lowest order.     

Maximally linear FIR digital differentiators

A new efficient algorithm for calculating the weighting coefficients of maximally linear, FIR digital differentiators is presented. Simple closed-form explicit and recursive formulas are derived in a very straightforward manner. Moreover, a simple recursive equation is established, relating coefficients of two digital differentiators of adjacent ranks.     

基于TMS320F28335的FIR-IFFT数字滤波方法

针对现有数字滤波方法存在大量傅里叶变换以及卷积运算,在工业控制领域处理50 Hz信号时,易造成处理器消耗大量运算时间,导致在低端处理器上无法实现常规数字滤波算法的问题,介绍了一种修改后的数字滤波算法,综合短时采样序列与最优窗函数在TMS320F28335上可快速实现该算法。经过窗函数截取后的信号进行FFT分析,去除谐波频率后IFFT还原波形,与通用的IIR或FIR滤波器相比,大幅缩短了程序运行时间,同时减少通用滤波器的大量卷积运算,提高程序执行效率。     

A technique for realizing linear phase IIR filters

A real-time IIR filter structure is presented that possesses exact phase linearity with 10~1000 times fewer general multiplies than conventional FIR filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay IIR filters. This structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real-time recursive implementation of the noncausal transfer function H(z^-1). The time reversed section technique used to realize exactly linear phase IIR filters is described. The effects of finite section length on the sectional convolution are analyzed. A simulation methodology is developed to address the special requirements of simulating a time reversed section filter. A design example is presented, with computer simulation to illustrate performance, in terms of overall magnitude response and phase linearity, as a function of finite section length. Nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct FIR implementation     

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.     

基于神经网络的4型FIR滤波器的优化设计

详细讨论了4型线性相位滤波器的幅频特性与正弦基函数神经网络算法的关系,分析了神经网络系统的稳定条件,给出了FIR滤波器优化设计实例。根据4型FIR滤波器的幅频响应特性,构造出一个相应的神经网络模型,并建立了FIR线性相位数字滤波器的神经网络算法。该算法通过训练神经网络权值,使设计的数字滤波器与希望得到的FIR线性相位滤波器的幅频响应之间的误差平方和最小化,从而获得FIR线性相位数字滤波器的脉冲响应。计算机仿真表明了该算法的有效性和优异性能。     

FIR数字滤波器的递推最小二乘设计算法

本文考虑对称系数及反对称系数的ＦＩＲ数字滤波器的设计问题,设计准则选为最小加权平方误差准则,并将这个设计问题看成一个线性系统的辨识问题,辨识系统参数所需的输入数据由一随机抽样法产生,辨识算法采用递推最小二乘法．按随机抽样法产生的数据具有很强的激励,保证了被辨识参数的收敛性,同时又自然地实现了最小加权平方误差准则．两个设计范例说明了本文提出的设计方法的有效性．     

一种基于迭代短卷积算法的低复杂度并行FIR滤波器结构

该文基于快速卷积算法,提出一种适用于线性相位FIR滤波器的并行结构。该结构采用快速卷积算法减少子滤波器个数,同时让尽可能多的子滤波器具有对称系数,然后利用系数对称的特性减少子滤波器模块中的乘法器数量。对于具有对称系数的FIR滤波器,提出的并行结构能够比已有的并行FIR结构节省大量的硬件资源,尤其当滤波器的抽头数较大时效果更明显。具体地,对一个4并行144抽头的FIR滤波器,提出的结构比改进的快速FIR算法(Fast FIR Algorithm, FFA)结构节省36个乘法器(14.3%),23个加法器(6.6%)和35个延时单元(11.0%)。     

Hardware efficient fast parallel FIR filter structures based on iterated short convolution

This paper presents an iterated short convolution (ISC) algorithm, based on the mixed radix algorithm and fast convolution algorithm. This ISC-based linear convolution structure is transposed to obtain a new hardware efficient fast parallel finite-impulse response (FIR) filter structure, which saves a large amount of hardware cost, especially when the length of the FIR filter is large. For example, for a 576-tap filter, the proposed structure saves 17% to 42% of the multiplications, 17% to 44% of the delay elements, and 3% to 27% of the additions, of those of prior fast parallel structures, when the level of parallelism varies from 6 to 72. Their regular structures also facilitate automatic hardware implementation of parallel FIR filters.     

基于FPGA的FIR升余弦滚降滤波器设计与实现

为了降低FIR滤波器对FPGA资源的消耗,同时能够直接验证其滤波性能。文中采用乘法器和加法器共享以及MEALY型状态机的实现方法,以及卷积、插零等算法,来实现FIR升余弦滚降滤波设计,同时给出了在Quartus II环境下的时序仿真结果。实践表明,此方法可以节省大量的FPGA资源,仅仅需要100多个LE逻辑单元,就可以有效解决FIR数字滤波器算法在FPGA设计中资源紧张的问题。     

FIR数字滤波器的一种快速算法

FIR数字滤波器本质上是一种线性卷积的运算,当数字滤波器的阶次N很大时,计算量很大,计算速度很慢,达不到系统对实时性的要求。文章介绍了一种数字信号处理算法,该算法将线性卷积运算转换成加法运算,利用加法运算进行求解,避免了数据堆积,加快了运算速度,从而使数字滤波器处理过程实时、快速。     

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。     

可变带宽FIR低通滤波器设计和RAG算法系数综合

提出使用简化加法器图算法综合可变带宽FIR数字滤波器。首先使用谱参数的方法建立可变带宽、线性相位的FIR低通数字滤波器的系统函数,通过使用加权最小均方的方法,得到了滤波器系数的最优表达式。然后基于可变滤波器结构为定系数FIR子滤波器线性组合的特点,提出使用筒化加法器图算法综合其硬件结构。该算法生成一种能最大程度地利用系数之间共享特性的加法器流图,使用较少的加法器个数和加法次数实现系数相乘。最后设计实例证明了可变带宽的有效性和该算法的高效性。     

基于Hanning Window设计FIR数字高通滤波器

基于实序列的傅里叶变换具有的特征,提出了一种研究线性相位FIR数字滤波器幅度函数的简洁方法。首先揭示了偶对称和奇对称的线性相位FIR数字滤波器幅度函数的特点;然后研究了矩形窗函数对线性相位理想数字低通滤波器幅频特性的影响,即时域加矩形窗,频域形成过渡带;最后介绍了利用窗函数法设计FIR数字滤波器时,对窗函数的要求,选择窗函数的依据及利用窗函数法设计FIR数字滤波器的步骤,并给出了基于Hanning Window来设计FIR数字高通滤波器的实例。     

A fast matrix iterative technique for the WLS design of 2-D quadrantally symmetic FIR filters

High computational complexity is a major problem encountered in the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters. In this paper, we present an iterative matrix solution with very low complexity to the weighted least square (WLS) design of 2-D quadrantally symmetric FIR filters with two-valued weighting functions. Firstly, a necessary and sufficient condition for the WLS design of 2-D quadrantally symmetric filters with general nonnegative weighting functions is obtained. Then, based on this optimality condition, a novel iterative algorithm is derived for the WLS design problem with a two-valued weighting function. Because the filter parameters are arranged in their natural 2-D form and the transition band is not sampled, the computation amount of the proposed algorithm is reduced significantly, especially for high-order filters. The exponential convergence of the algorithm is established, and its computational complexity is estimated. Design examples demonstrating the convergence rate and solution accuracy of the algorithm, as well as the relation between the iteration number of the algorithm and the size and transition-band width of the filter are given.     

A robust O(N log n) algorithm for optimal decoding of first-orderΣ-Δ sequences

An exact recursive formula is derived to describe the structure of an ideal first-order Σ-Δ output sequence as a function of its input. Specifically, it is shown that every Σ-Δ sequence generated by the constant input x∈[0, 1] can be decomposed into a shorter E-A subsequence whose input x'∈[0, 1) may be used to recover that of the original Σ-Δ sequence. This formula is applied to develop an O(N log N) algorithm for decoding an N-length sequence. Without knowledge of the modulator's initial state, it exhibits an average improvement, over all initial states, of 4.2 dB in output signal-to-noise ratio (SNR) compared with a near-optimal linear finite impulse response (FIR) filter. The regularity of the ideal first-order Σ-Δ structure with constant inputs permits the algorithm to be extended to bandlimited and noise-corrupted data. A simple error correction procedure is demonstrated, and it is shown that the recursive algorithm can outperform FIR filters on sequences of length N<64 having input SNRs as low as 30 dB     

The recursive pyramid algorithm for the discrete wavelet transform

The recursive pyramid algorithm (RPA) is a reformulation of the classical pyramid algorithm (PA) for computing the discrete wavelet transform (DWT). The RPA computes the N-point DWT in real time (running DWT) using just L(log N-1) words of storage, as compared with O(N) words required by the PA. L is the length of the wavelet filter. The RPA is combined with the short-length FIR filter algorithms to reduce the number of multiplications and additions     

ARMA implementation of diffraction operators with inverse-rootsingularities

The integral of a time-domain diffraction operator which has an integrable inverse-root singularity and an infinite tail is numerically differentiated to get a truncated digital form of the operator. This truncated difference operator effectively simulates the singularity but is computationally inefficient and produces a convolutional truncation ghost. The authors therefore use a least-squares method to model an equivalent autoregressive moving-average (ARMA) filter on the difference operator. The recursive convolution of the ARMA filter with a wavelet has no truncation ghost and an error below 1% of the peak diffraction amplitude. Design and application of the ARMA filter reduces computer (CPU) time by 42% over that repaired with direct convolution. A combination of filter design at a coarse spatial sampling, angular interpolation of filter coefficients to a finer sampling, and recursive application reduces CPU time by 83% over direct convolution or 80% over Fourier convolution, which also has truncation error     

An unbiased p-step predictive FIR filter for a class of noise-free discrete-time models with independently observed states

The paper addresses a new unbiased p-step toward predictive finite impulse response (FIR) filter for a class of discrete-time deterministic state space models, which states are represented on a horizon of N past points with degree polynomials and observed independently. It is implied that measurements are not available at a current time point n. The problem arises in synchronization and tracking when a signal is lost. Generic coefficients are derived via the Bernoulli polynomials for a two-parameter family of the polynomial filter gains. A generalization is provided for the linear (ramp) and quadratic filter gains. We show that the solution proposed is efficient in applications to predictive filtering of the states of local clocks of digital communication network nodes when a synchronizing signal is temporarily not available.     

Analytical design method for optimal equiripple comb FIR filters

A novel analytical design method for highly selective digital optimal equiripple comb finite-impulse response (FIR) filters is presented. The equiripple comb FIR filters are optimal in the Chebyshev sense. The number of notch bands, the width of the notch bands and the attenuation in the passbands can be independently specified. The degree formula and the differential equation for the generating polynomial of the filter is presented. Based on the differential equation, a fast simple algebraic recursive procedure for the evaluation of the impulse response of the filter is described. Its arithmetic robustness outperforms, by far, the known analytical design method. Highly selective equiripple comb FIR filters with thousands of coefficients can be designed. One example demonstrates the efficiency of the filter design.