Design of arbitrary-phase variable digital filters using SVD-based vector-array decomposition

This paper proposes a straightforward method for designing variable digital filters with arbitrary variable magnitude as well as arbitrary fixed-phase or variable fractional delay (VFD) responses. The basic idea is to avoid the complicated direct design of one-dimensional (1-D) variable digital filters by decomposing the original variable filter design problem into easier subproblems that only require constant 1-D filter designs and multidimensional polynomial approximations. Through constant 1-D filter designs and multidimensional polynomial fits, we can easily obtain a variable digital filter satisfying the given variable design specifications. To decompose the original variable filter design into constant 1-D filter designs and multidimensional polynomial fits, a new multidimensional complex array decomposition called vector array decomposition (VAD) is proposed, which is based on two new theorems using the singular value decomposition (SVD). Once the VAD is obtained, the subproblems can be easily solved. Furthermore, we show that the VAD can also be generalized to the weighted least squares (WLS) case (WLS-VAD) for the WLS variable filter design. Three design examples are given to illustrate that the WLS-VAD and VAD-based techniques are considerably efficient for designing variable digital filters with arbitrary variable magnitude and arbitrary fixed-phase or VFD responses.     

Variable digital filter design using the outer product expansion

Digital filters with adjustable frequency domain characteristics are referred to as variable digital filters. Variable filters are useful in the applications where the filter characteristics are required to be changeable during the course of signal processing. Especially in real time applications, variable filters are needed to change their coefficients instantaneously such that the real time signal processing can be performed. The present paper proposes a very efficient technique for variable 1D digital filter design. Generally speaking, the variable coefficients of variable digital filters are multidimensional functions of a set of spectral parameters which define the desired frequency domain characteristics. The authors first sample the given variable 1D magnitude specification and use the samples to construct a multidimensional array, then propose an outer product expansion method for expanding the multidimensional array as the sum of outer products of 1D arrays (vectors). Based on the outer product expansion, one can reduce the difficult problem of designing a variable 1D digital filter to the easy one that only needs constant 1D filter designs and 1D polynomial approximations. The technique can obtain variable 1D filters having arbitrary desired magnitude characteristics with a high design accuracy     

The design of arbitrary FIR digital filters using the eigenfiltermethod

The design of finite impulse response (FIR) digital filters for approximating an arbitrary function (in both magnitude and phase) in the least-square sense is studied. The design method is based on the computation of an eigenvector of an appropriate real, symmetric and positive-definite matrix. The design of the complex-coefficient filter is shown to be an extension of the design of the real-coefficient filter. Several design examples, including the constant-group-delay filters and digital phase all-pass filters, are presented. Comparisons to existing methods are made     

Optimal synthesis of multidimensional state-space digital filters: A general analysis

The optimal synthesis of a single-input single-output (SISO) multidimensional (M-D) digital filter with fixed-point arithmetic is investigated. The necessary and sufficient conditions for optimal realizations for both optimal and equal wordlength registers are established. It is shown that these optimality conditions always can be satisfied for an arbitrary M-D filter. It is proven that optimal structures possess some favorable properties such as low coefficient sensitivity. It is found that the optimal realizations of a multidimensional filter demonstrate a remarkable property in needed number of multipliers per sample output is comparison to one dimensional (1-D) optimal structures. Two numerical examples are presented to illustrate the design procedure and usefulness of the proposed scheme.     

全相位DFT数字滤波器的设计与实现

本文提出了全相位数据空间的概念,并基于DFT/IDFT滤波导出了一种新型的零相位滤波器——全相位DFT(APDFT)数字滤波器.本文给出了它的脉冲响应与相应的DFT滤波响应向量之间的正、反变换公式,证明了这种滤波器的一些重要性质.APDFT方法兼有窗函数法和频率采样法的优点,是一种设计FIR滤波器的新方法.理论分析和模拟实验证实,其总体性能优于传统方法.APDFT数字滤波器除可用通常的卷积结构实现外,也可用一种直接频域网络实现.本文给出了这种网络结构及其简化算法.这种网络具有实时自设计功能.它可以构成时变系统用于滤波器传递函数实时可变的场合,可以方便地集成为一个长度和频响均可编程的通用零相位数字滤波器,而且还可用于实现严格互补子带滤波.     

软件无线电数字中频处理的优化设计

软件无线电是目前通信领域研究的热点,其关键技术之一数字中频技术是多速率信号处理理论的典型应用。本文研究了窄带信号条件下,高倍抽取的数字下变频设计,重点分析了基于CIC滤波器和HB滤波器的多级抽取算法。经比较,该设计比单级多相抽取设计节省98.8％的资源,完全可在单片FPGA内实现,而且,滤波性能优于设计指标要求。     

Design techniques for high-speed multirate multistage FIR digital filters

This paper presents architecture design techniques for implementing both single-rate and multirate high-speed finite impulse response (FIR) digital filters, with emphasis on the multirate multistage interpolated FIR (IFIR) digital filters. Well-known techniques to achieve high-speed and low-power applications for the single-rate digital FIR architecture are summarized, followed by the introduction of variable filter order selection, optimal filter decomposition, memory-saving and mirror symmetric filter pairs techniques which offer further gains in both performance and complexity reduction for the multirate multistage digital FIR architecture. A filter design example with TSMC 0.25?µm standard cell for 64-QAM baseband demodulator shows that the area is reduced by 39% for low-complexity application. Moreover, for high-speed application, the chip can operate at 714?MHz. Finally, a designed decimator which is used in the CDMA cellular shows that the area is reduced by 70% as compared with conventional approach.     

一种基于噪声估计的语音激活检测算法

针对当前语音激活检测算法在低信噪比和复杂噪声模型的环境下性能损失的问题,提出了一种基于噪声估计的语音激活检测算法,通过对背景噪声进行自适应估计,得到准确的信噪比门限,同时利用估计背景噪声对短时谱进行白化处理,从而使得谱熵判决准则得以适用于复杂噪声模型的环境。实验证明,算法在低信噪比和复杂噪声模型下性能优于G.729B和AMR中的语音激活检测算法。     

空时自适应杂波分类抑制与弱小运动目标检测

提出了一种新的方法应用于一类重要的高维信号检测问题:在强杂波干扰下检测数字图像序列中位置和速度未知的弱小运动目标.通过对输入序列时域灰度矩进行学习,将像素分成两类———静杂波和动杂波.分别对其采用非参数时域滤波和LS自适应滤波进行去除,从而将原始数据转化为准SPGWN模型.杂波抑制后,根据单帧多像素目标模型假设,采用在空、时域联合集成信号能量的检测算法,能有效地改善信噪比并且有利于实时实现.理论分析和对真实数据的大量仿真试验验证了本方法的有效性.     

Design of separable-denominator 2-D digital filters using the reduced-dimensional decomposition model

A separable-denominator 2-D digital filter (SD-2DDF) can be decomposed into the cascade form of a pair of 1-D digital filters (1DDFs) with different delay elements. Based on this reduced-dimensional decomposition, in this paper, we propose a new technique for designing SD-2DDFs in the spatial domain. The technique determines the coefficient matrices of 1DDFs by nonlinear optimization techniques first, and then a SD-2DDF can be easily synthesized. In addition, since the existent 1-D linear system realization techniques can be used to choose a good starting point for the optimization, extremely accurate design results can be easily achieved.     

CORDIC-lifting factorization of paraunitary filter banks based on the quaternionic multipliers for lossless image coding

Quaternions have offered a new paradigm to the signal processing community: to operate directly in a multidimensional domain. We have recently introduced the quaternionic approach to the design and implementation of paraunitary filter banks: four- and eight-channel linear-phase paraunitary filter banks, including those with pairwise-mirror-image symmetric frequency responses. The hypercomplex number theory is utilized to derive novel lattice structures in which quaternion multipliers replace Givens (planar) rotations. Unlike the conventional algorithms, the proposed computational schemes maintain losslessness regardless of their coefficient quantization. Moreover, the one regularity conditions can be expressed directly in terms of the quaternion lattice coefficients and thus easily satisfied even in finite-precision arithmetic. In this paper, a novel approach to realizing CORDIC-lifting factorization of paraunitary filter banks is presented, which is based on the embedding of the CORDIC algorithm inside the lifting scheme. Lifting allows for making multiplications invertible. The 2D CORDIC engine using sparse iterations and asynchronous pipeline processor architecture based on the embedded CORDIC engine as stage of processor is reported. Also it is necessary to notice, that the quaternion multiplier lifting scheme based on the 2D CORDIC algorithm is the structural decision for the lossless digital signal processing. This approach applies to very practical filter banks, which are essential for image processing, and addresses interesting theoretical questions.     

Digital Filter Design Using Computer Algebra Systems

Digital filter design can be performed very efficiently using modern computer tools. The drawback of the numeric-based tools is that they usually generate a tremendous amount of numeric data, and the user might easily lose insight into the phenomenon being investigated. The computer algebra systems successfully overcome some problems encountered in the traditional numeric-only approach. In this paper, we introduce an original approach to algorithm development and digital filter design using a computer algebra system. The main result of the paper is the development of an algorithm for an infinite impulse response (IIR) filter design that, theoretically, is impossible to be implemented using the traditional approach. We present a step-by-step procedure which includes derivations of closed-form expressions for (1) the transfer functions of the implemented digital filter which contains the algebraic loop; (2) the closed-form expression for computing the number of requested iteration steps; and (3) the error function representing the difference of the output sample values of the new filter and that of the conventional filter. We demonstrate how one can use some already-known multiplierless digital filter as a start-up filter to design a new digital filter whose passband edge frequency can be simply moved by using a single parameter. As a result, we obtain a multiplierless IIR filter, which belongs to the family of low-power digital filters where multipliers are replaced with a small number of adders and shifters.     

Design of 2-D FIR narrow transition band filters by double transformations using GA approach

In this investigation, subfilters are cascaded in the design of a 2-D narrow transition band FIR digital filter with double transformations, a transformation from wide transition band subfilter into 1-D narrow transition band filter and a McClellan transformation from 1-D filter into 2-D filter. The traditional method for designing a 2-D FIR digital filter with a narrow transition band yields very high orders. The difficulty of the design and implementation will increase with orders exponentially. Numerous identical low-order subfilters are cascaded together to simplify the design of a high-order 2-D filter compared to traditional design method. A powerful genetic algorithm (GA) is presented to determine the best coefficients of the McClellan transformation. It can be used to design any contours of arbitrary shape for mapping 1-D to 2-D FIR filters very effectively. A generalized McClellan transformation is presented, and can be used to design 2-D complex FIR filters. Various numerical design examples are presented to demonstrate the usefulness and effectiveness of the presented approach.

Noniterative WLS design of allpass variable fractional-delay digital filters

This paper presents a noniterative weighted-least-squares (WLS) method for designing allpass variable fractional-delay (VFD) digital filters. After expressing each coefficient of an allpass VFD filter as a polynomial of the VFD parameter p, we develop a noniterative technique for finding the optimal polynomial coefficients, and show that the allpass VFD filter design problem can be efficiently solved without using any iterative procedure while a closed-form solution can be easily obtained through solving a matrix equation. Compared with the existing iterative WLS method that solves a series of approximately linearized WLS minimization problems, the proposed noniterative one can yield much better design results with significantly reduced computational complexity. Moreover, the new WLS method does not involve any convergence issue.     

Unified theory of symmetry for two-dimensional complex polynomials using delta discrete-time operator

The complexity in the design and implementation of 2-D filters can be reduced considerably if the symmetries that might be present in the frequency responses of these filters are utilized. As the delta operator (??-domain) formulation of digital filters offers better numerical accuracy and lower coefficient sensitivity in narrow-band filter designs when compared to the traditional shift-operator formulation, it is desirable to have efficient design and implementation techniques in ??-domain which utilize the various symmetries in the filter specifications. Furthermore, with the delta operator formulation, the discrete-time systems and results converge to their continuous-time counterparts as the sampling periods tend to zero. So a unifying theory can be established for both discrete- and continuous-time systems using the delta operator approach. With these motivations, we comprehensively establish the unifying symmetry theory for delta-operator formulated discrete-time complex-coefficient 2-D polynomials and functions, arising out of the many types of symmetries in their magnitude responses. The derived symmetry results merge with the s-domain results when the sampling periods tend to zero, and are more general than the real-coefficient results presented earlier. An example is provided to illustrate the use of the symmetry constraints in the design of a 2-D IIR filter with complex coefficients. For the narrow-band filter in the example, it can be seen that the ??-domain transfer function possesses better sensitivity to coefficient rounding than the z-domain counterpart.     

A novel nonnegative decomposition method and its application to 2-D digital filter design

In designing two-dimensional (2-D) digital filters in the frequency domain, an efficient technique is to first decompose the given 2-D frequency domain design specifications into one-dimensional (1-D) ones, and then approximate the resulting 1-D magnitude specifications using the well-developed 1-D filter design techniques. Finally, by interconnecting the designed 1-D filters one can obtain a 2-D digital filter. However, since the magnitude responses of digital filters must be nonnegative, it is required that the decomposition of 2-D magnitude specifications result in nonnegative 1-D magnitude specifications. We call such a decomposition the nonnegative decomposition. This paper proposes a nonnegative decomposition method for decomposing the given 2-D magnitude specifications into 1-D ones, and then transforms the problem of designing a 2-D digital filter into that of designing 1-D filters. Consequently, the original problem of designing a 2-D filter is significantly simplified.     

Variable Fractional Delay Filter Design Using a Symmetric Window

In this paper a numerically efficient method for designing a nearly optimal variable fractional delay (VFD) filter based on a simple and well-known window method is presented. In the proposed method a single window extracted from the optimal filter with fixed fractional delay (FD) is divided into even and odd part. Subsequently, the odd part is discarded and symmetric even part of the extracted window is used to design a family of nearly optimal filters with varying FD. In addition to window extraction, the proposed approach requires filter gain correction which is dependent on the desired FD. Optimum values of the gain correction factor as well as the extracted window can be computed beforehand, which allows us to design a nearly optimal FD filter with arbitrary FD at low numerical costs during runtime. On the basis of the proposed filter design method, the universal structure of VFD filter allowing for change of filter type and length has been proposed. In the paper, three FD filter optimality criteria are considered, which are maximal flatness, Chebyshev (minimax), and least squares.     

A simple adaptive algorithm for real-time processing in antenna arrays

A new adaptation algorithm designed for real-time data processing in large antenna arrays is presented. The algorithm is used to determine the set of filter coefficients (weights) which minimizes the mean-square error in a multidimensional linear filter. The algorithm forms an estimate of the target signal, which is assumed to be of interest, in the presence of interfering noises. It is assumed that the direction of arrival and spectral density of the target signal are known a priori. No such information is assumed to be available regarding the structure of the interfering noise field. The a priori target information is incorporated directly into the adaptation procedure using a modified gradient descent technique. The mathematical convergence properties of the algorithm are presented and a computer simulation experiment is used as an illustration. It is shown that as the number of iterations becomes large, the expected value of the adaptive solution converges to the minimum mean-square-error solution. It is further shown that the variance of the adapted filter about the optimum solution can be made arbitrarily small by appropriate choice of a scalar constant in the algorithm. These results are based on the assumption that the array signals are Gaussian and that successive time samples are statistically uncorrelated. Thus, the new algorithm is shown to converge to the optimum processor in the limit as the number of adaptations becomes large. Any disadvantage which may arise in the use of such an asymptotically optimum system is offset by the extreme simplicity of the adaptive procedure. This simplicity should prove to be particularly useful in many of the practical array processing problems recently encountered in seismic and sonar data processing.     

基于子阵结构的大孔径相控阵天线设计

在卫星通信和飞行器测控中,大孔径相控阵天线结构上采用前端模拟子阵和阵间数字波束形成相结合的方式,可以克服天线面临的时间色散问题。子阵规模通过成本和子阵色散确定,阵间波束形成采用空时二维延时滤波器结构,滤波器系数采用查找表方式获得,便于工程实现。计算机仿真验证了系统结构、子阵划分、延时滤波器设计的正确性。     

子带分解的自适应滤波器的FPGA实现

基于子带分解的自适应滤波器在提高收敛性能的同时又可以节省一定的计算量。采用Altera 公司的仿真软件Altera DSP Builder 和Quartus Ⅱ7.2进行子带分解的NLMS算法的自适应滤波器现场可编程门阵列设计, 利用Simulink和ModelSim对设计方案进行了模型仿真和功能仿真,达到较好的效果。