Extending the concept of IIR filtering to array processing using approximate spatial IIR structure

Various array processing techniques applied to uniform linear arrays are involuntarily realized using structures that are analogous to finite impulse response filters. This observation leads to the following question: “can we extend infinite impulse response (IIR) filtering to array processing?”. In this paper, we introduce the concept of IIR array in spatial domain. Note that IIR array here does not mean time-domain IIR filtering for array beamforming which is commonly understood. This paper is dedicated to the study of an alternate approach for array signal processing which defines IIR structure in spatial domain. To illustrate the applicability of the concept of IIR array, we propose a new direction-of-arrival estimation technique as well as a beamformer with the spatial domain IIR array implementation. The performance of the proposed methods are comparable to the existing techniques. These illustrations are intended to introduce a new approach which potentially can offer more degrees of freedom to control the performance of the array and reduce the complexity of the system for a desired performance.     

Two Classes of Cosine-Modulated IIR/IIR and IIR/FIR NPR Filter Banks

This paper introduces two classes of cosine-modulated causal and stable filter banks (FBs) with near perfect reconstruction (NPR) and low implementation complexity. Both classes have the same infinite-length impulse response (IIR) analysis FB but different synthesis FBs utilizing IIR and finite-length impulse response (FIR) filters, respectively. The two classes are preferable for different types of specifications. The IIR/FIR FBs are preferred if small phase errors relative to the magnitude error are desired, and vice versa. The paper provides systematic design procedures so that PR can be approximated as closely as desired. It is demonstrated through several examples that the proposed FB classes, depending on the specification, can have a lower implementation complexity compared to existing FIR and IIR cosine-modulated FBs (CMFBs). The price to pay for the reduced complexity is generally an increased delay. Furthermore, two additional attractive features of the proposed FBs are that they are asymmetric in the sense that one of the analysis and synthesis banks has a lower computational complexity compared to the other, which can be beneficial in some applications, and that the number of distinct coefficients is small, which facilitates the design of FBs with large numbers of channels.     

Reduced order IIR approximation to FIR digital filters

An algorithm for designing an infinite-impulse-response (IIR) stable filter using a finite-impulse-response (FIR) given filter, with the objective of reducing the delay and order, is described. The design is in the time domain using the least-squares-inverse algorithm, which is briefly described. In this method, the numerator of the approximated filter is part of the FIR filter itself and no calculations and minimization are needed to find the numerator coefficients (except finding the FIR roots). An error analysis between the given FIR and approximated IIR filters is provided. This error analysis enables the designer to fix a design parameter, often unnoted, keeping the energies of the approximated and original filters equal. Results and two illustrative examples are presented     

一种设计IIR数字滤波器的参数化方法

 基于连续时间状态空间结构和广义双线性变换,提出了一种设计无限冲激响应(IIR)数字滤波器的参数化方法.优点是稳定区域包含了整个参数空间,因此可以采用无约束优化方法.给出了仿真实例,并与已有的设计方法进行了比较,其通带波动、阻带衰减、群迟延等性能更为优越.     

IIR数字滤波器仿真实现

数字滤波技术是数字信号处理的一个重要组成部分,滤波器的设计是信号处理的核心问题之一。本文分析了在MATLAB环境下无限脉冲响应（IIR）数字滤波器设计的设计方法及仿真实现。     

Transform domain IIR filtering

The paper provides a generalization on the concept of the transform domain filtering (TDF). TDF is block-based filtering, or vector-filtering, applied to transform domain data to get the effect of desired time domain filtering. The result is transform domain IIR filtering (IIR-TDF) and it takes in the existing TDF, or FIR-TDF, as its special case. The resulting structures are two-fold-direct I form and direct II form-and are both block-filtering structures     

非高斯噪声下的一种自适应IIR滤波算法

给出一种用递归总体最小平均P-范数法来实现IIR滤波器的估计,在估计中采用power迭代法,并应用矩阵求逆引理克服了直接求逆的繁琐计算,在文章的最后给出计算机仿真,显示了该算法性能的优越性。     

数字IIR滤波器FIR逼近的LMI方法

基于有界实引理（BRL）,使FIR滤波器逼近数字IIR滤波器问题变换为具线性矩阵不等式（LMI）约束的凸次优化问题,提出了具H∞误差范数的IIR滤波器FIR逼近方法,数值计算证实了该方法的有效性。     

针对窄带干扰抑制的数字陷波器设计

现代扩频技术中,由于带宽和技术方面限制了扩频处理增益,使得固有的抗干扰性能得不到更好发展,因此设计滤波器抑制窄带干扰是信息处理的关键技术之一。在分析一般2阶IIR陷波器设计方法的基础上,提出一种新颖的数字外差滤波器,其思想来源于通信系统中的调制解调,在结构和算法上不同于一般处理技术,而且能控制馅波深度和宽度这样的参数。从理论推导及仿真试验都可以看出,这种滤波器系统稳定、灵敏度高,能够较好地滤除窄带干扰的影响。     

New orthogonalised IIR adaptive filter

A new IIR-ADF algorithm is proposed in which the discrete cosine transform, a fairly good approach of KLT for a large number of signal classes, is used to split the input signal into a set of nearly orthogonal transform coefficients. Subsequently these coefficients are filtered by a bank of IIR-ADFs whose coefficients are independently updated to minimise a common error. Computer simulations show that the proposed algorithm provides a faster convergence rate than the Gauss-Newton algorithm with a much reduced computational load     

Adaptive lattice-form IIR blind equaliser

The author describes incorporation of the lattice-form structure in the blind infinite impulse response (IIR) algorithm, based on a cost function which is a modified version of that proposed by Shalvi and Weinstein (1990). The proposed IIR blind equaliser has the advantage of lower complexity; simulation results also indicate that the proposed IIR blind equaliser has a faster convergence rate and a smaller mean square error (MSE)     

收敛的级联形式自适应IIR滤波器

本文主要研究基于级联形式实现的自适应ＩＩＲ滤波器，分别讨论预测误差算法和利用预测误差及新的收敛梯度对ＡＩＩＲＦ参数估计算法的级联ＡＩＩＲＦ。与直接形式实现的ＡＩＩＲＦ相比，级联ＡＩＩＲＦ可直接对其极点估计检测，从而确保ＡＩＩＲＦ的稳定性，新算法的参估计可以收敛于全局最优解，解决了输出误差算法中的多局部极小点问题。     

Cascade lattice IIR adaptive filters

The feedback lattice filter forms, including the two-multiplier form and the normalized form, are examined with respect to their relationships to the feedback direct form filter. Specifically, the transformation matrix between the lattice forms and the direct form is derived; parameter and state relationships between the lattice forms and the direct form are therefore obtained. An IIR filter structure-the cascade lattice IIR structure-is constructed. Based on this structure, three IIR adaptive filtering algorithms in the two-multiplier form can then be developed following the gradient approach, the Steiglitz-McBride approach and the hyperstability approach. Convergence of these algorithms is theoretically analyzed using either the ODE approach or the hyperstability theorem. These algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms. Relationships of the simplified algorithms to the direct form algorithms are also studied, which disclose a consistency in algorithm structure regardless of the filter form. Three normalized lattice algorithms can also be derived from the two-multiplier lattice algorithms. Experimental results show much improved performance of the normalized lattice algorithms over the two-multiplier lattice algorithms and the direct form algorithms     

改进的IIR滤波器避免运算溢出和定点DSP的实现

数字滤波器的设计是数字信号处理(DSP)领域的一个重要部分.在用定点DSP器件设计数字滤波器时,一个重要的问题,就是由于硬件字长精度有限,运算会出现溢出,因此在选择恰当的滤波器的定标参数后,必须注重选取有效的结构,以保证有足够的计算精度和避免运算溢出.     

Theory of rate-distortion-optimal, constrainedfilterbanks-application to IIR and FIR biorthogonal designs

We design filterbanks that are best matched to input signal statistics in M-channel subband coders, using a rate-distortion criterion. Previous research has shown that unconstrained-length, paraunitary filterbanks optimized under various energy compaction criteria are principal-component filterbanks that satisfy two fundamental properties: total decorrelation and spectral majorization. In this paper, we first demonstrate that the two properties above are not specific to the paraunitary case but are satisfied for a much broader class of design constraints. Our results apply to a broad class of rate-distortion criteria, including the conventional coding gain criterion as a special case. A consequence of these properties is that optimal perfect-reconstruction (PR) filterbanks take the form of the cascade of principal-component filterbanks and a bank of pre- and post-conditioning filters. The proof uses variational techniques and is applicable to a variety of constrained design problems. In the second part of this paper, we apply the theory above to practical filterbank design problems. We give analytical expressions for optimal IIR biorthogonal filterbanks; our analysis validates a conjecture by several researchers. We then derive the asymptotic limit of optimal FIR biorthogonal filterbanks as filter length tends to infinity. The performance loss due to FIR constraints is quantified theoretically and experimentally. The optimal filters are quite different from traditional filters. Finally, a sensitivity analysis is presented     

An IIR median hybrid filter

A new class of nonlinear filters, the multidirectional infinite impulse response median hybrid (MIMH) filters, is presented and analyzed. The input signal is processed twice using a linear shift-invariant (LSI) infinite impulse response (IIR) filtering module: once with normal causality and a second time with inverted causality. The final output of the MIMH filter is the median of the two-directional outputs and the original input signal. Thus, the MIMH filter is a concatenation of linear filtering (a LSI IIR filtering module) and nonlinear filtering (a median filtering module). Because of this unique scheme, the MIMH filter possesses many desirable properties which are both proven and analyzed (including impulse removal, step preservation, and noise suppression). A comparison to other medium-type filters is also provided     

Low-Order IIR Filter Bank Design

The advantage of infinite-impulse response (IIR) filters over finite-impulse response (FIR) ones is that the former require a much lower order (much fewer multipliers and adders) to obtain the desired response specifications. However, in contrast with well-developed FIR filter bank design theory, there is no satisfactory methodology for IIR filter bank design. The well-known IIR filters are mostly derived by rather heuristic techniques, which work in only narrow design classes. The existing deterministic techniques usually lead to too high order IIR filters and thus cannot be practically used. In this paper, we propose a new method to solve the low-order IIR filter bank design, which is based on tractable linear-matrix inequality (LMI) optimization. Our focus is the quadrature mirror filter bank design, although other IIR filter related problems can be treated and solved in a similar way. The viability of our theoretical development is confirmed by extensive simulation.     

Polyphase SC IIR Hilbert transformers

A novel polyphase switched-capacitor (SC) implementation of IIR Hilbert transformers is proposed. The circuit employs fewer op-amps and has better performance than the traditional two-phase circuit. SWIT-CAP2 simulation results and phase sensitivities to capacitance mismatches are provided     

IIR滤波器的定点设计方法

通过一个已经成功地应用于移动通信系统的IIR滤波器的设计实例，说明了在通用DSP处理器仅支持定点运算且该处理器的字长有限的前提下，如何保证IIR滤波器的稳定性，以及如何保证滤波器在运算过程中不会发生溢出。