Adaptive IIR Filters Research Articles

A Structural View of Stability in Adaptive IIR Filters

This correspondence deals with the stability issue in adaptive IIR filters from a structural view. A new condition, under which the bounded-input bounded-output (BIBO) stability of the filters can be ensured, is derived. Based on this result, a normal state-space realization for second-order IIR filters is proposed. It is shown that the adaptive IIR filter realized with such a structure is BIBO stable no matter it is implemented with infinite or finite precision. This property is very important for real-time applications. Though both the proposed and the normalized lattice-based structures are BIBO stable, the former is simpler and has minimal pole sensitivities. Two adaptive IIR filter structures are developed based on a cascade form of second-order filters. The first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters. Simulations are given to demonstrate the performance of the proposed structures

Recursive total instrumental-variable algorithm for solving over-determined normal equations and its applications

The well-known recursive least-squares (RLS) algorithms are directly dependent on the recursive estimation method for inversion of the auto-correlation matrix based on the matrix inverse lemma. On the basis of recursive estimation of the augmented cross-correlation matrix and the well-known power iteration, this paper establishes a recursive total instrumental-variable (RTIV) algorithm for tracking the total least-squares (TLS) solution of the normal equations in the over-determined instrumental-variable methods. Under the condition that the recursive estimation of the augmented cross-correlation matrix is asymptotically convergent, we show that the weight vector in the RTIV algorithm converges to the direction parallel to the singular vector associated with the smallest singular value of the augmented cross-correlation matrix. When the algorithm is applied in a parameter estimation problem, the converging weight vector corresponds to the TLS solution of the over-determined normal equations. Since the estimated parameters are optimal in the TLS sense, in the case where noise exists in both the input and output of the system or with the short sampling data, its noise rejection capability is superior to that of least-squares-based algorithms. The applicability and performance of the RTIV algorithm are demonstrated by computer simulations for adaptive IIR filtering and harmonic retrieval.

능동머플러를 위한 안정한 다중채널 적응 IIR 필터

In this paper, implementation of active mufflers using multiple channel adaptive IIR filter is presented. Usually, recursive LMS(RLMS) algorithms for adaptive IIR filters are highly efficient than filtered-X LMS(FXLMS) algorithms, when the order of both algorithms are the same. However, RLMS algorithms usually diverge before the algorithms arenot yet converged. So, the prefilters are presented to improve the stability by pulling the poles of feedback control transfer function in the beginning of active noise control and returning the original poles after the filters converge. The engine noises of diesel engine automobiles and gasoline engine automobiles are analyzed and the mathematical model of an active muffler is derived. Computer simulations and experiments are performed to show the effectiveness of the proposed systems.

Comparison of convergence characteristics of adaptive IIR and FIR filters for active noise control in a duct

There are perceived drawbacks to using adaptive IIR filters, as opposed to adaptive FIR filters, for active noise control (ANC). These include stability issues, the possible convergence of estimated parameters to biased and/or local minimum solutions and relatively slow rate of convergence. Stability issues can generally be resolved easily using well-established methods. In this Technical Note convergence rates are compared with particular reference to the active control of noise in a duct, for which the dynamics of the cancellation path are important. The characteristics of this application of ANC set it apart from usual signal processing applications of adaptive IIR filters and this has implications for the convergence properties. Various control approaches are considered: IIR least mean squares (IIR-LMS), IIR recursive least squares (IIR-RLS) with FASPIS (Fast Algorithm Secondary Path Integration Scheme) and FIR-LMS. Numerical examples are presented. It is seen that the cancellation path dynamics generally have the effect of changing the performance surface of the estimated IIR filter from bimodal to unimodal, which has consequences for improving the convergence rate of adaptive IIR filters. It is also seen that IIR-RLS has a comparable rate of convergence to FIR-LMS, with the steady-state performance being as good or better.

A new IIR adaptive notch filter

A new IIR adaptive notch filter (ANF) with fast convergence rate, accurate estimation of notch frequencies, and modest realization complexity is presented in this paper. The problem of obtaining a notch filter from a given signal containing multiple sine waves in noise is first formulated as the conventional problem of system identification. Then the new ANF is developed via the algorithm of Steiglitz McBride. Extensive simulations have been performed to verify the effectiveness of the ANF.

Global Stability of Adaptive IIR Filters Based on the Output Error Method and Parameter Truncation

This paper presents a rigorous proof of global stability of an adaptive infinite impulse response filter based on the output error method. The underlying idea of the developed analysis is the construction of suitable Lyapunov functions for different phases of adaptation. The considered estimator is an algorithm with a nonvanishing gain sequence. In order to prevent drift along an unstable manifold, a truncation of parameter estimates is incorporated. Such an algorithm is suitable for nonstationary signals.

A Novel All-Digital PLL With Software Adaptive Filter

The phase-locked loop (PLL) is one of the key building blocks of modern electronic designs. This paper presents a novel PLL structure that utilizes a flying-adder frequency synthesizer as its digital control oscillator (DCO), a software implemented adaptive IIR filter as its loop filter, and a unique counter as its phase detector. This all-digital PLL (ADPLL) achieved the desired functionality with additional advantages including no off-chip R and C components required, dynamic control of the loop gain on the fly, easy implementation on the digital CMOS process. This paper presents detailed descriptions of each component of this ADPLL; it also presents the system modeling in Z-domain, by mapping from S-domain, for dynamic response, stability, and steady-state error study.

IIR adaptive line enhancer filters for detection of gravitational waves from coalescing binaries

In this paper, we discuss the performances of infinite impulse response adaptive line enhancer (IIR ALE) filters compared with those of standard matched filters for detection of gravitational waves (GW) generated by coalescing binaries (CB). This comparison was performed with the help of numerical simulation, necessary to also provide a statistical characterization of the adaptive filters. The results of this preliminary analysis are also quite promising in connection with the relatively small computational power needed coupled with the robustness of these algorithms. In fact, a first possible and effective application of these filters is their use as real-time triggers for selecting candidates for further intensive analysis based on standard optimal methods.

Real-time room acoustic response simulation by IIR adaptive filter

A new IIR adaptive filter for real-time, room acoustic response simulation is proposed, the structure of which derives from Jot's model of an artificial reverberator. The simultaneous perturbation stochastic approximation (SPSA) algorithm is used to set parameter values. Results show good similarity between the desired and artificial response.

On the uniqueness of stationary points in L2 approximation with a rational polyphase function

The question of uniqueness of L 2 approximation when using a rational polyphase function is of great importance for the practical use of polyphase IIR adaptive filters. As shown in a previous work, the polyphase structure can alleviate the problem of convergence speed in IIR adaptive filters, allowing their computational complexity gain over FIR adaptive filters to be exploited. In that work, however, a demonstration of a uniqueness property was not presented. In this paper, we initially present an example of a practical application and the gain in convergence speed that can be achieved by using a polyphase IIR adaptive filter. We then demonstrate the following uniqueness property of the approximation of a rational function with degree N by a p-phase rational polyphase function with pM+1 and M free coefficients in, respectively, its numerator and denominator: if N is less or equal to M then the two functions are identical at all stationary points of the squared L 2 norm of the error. Following the demonstration of the uniqueness property, we make some remarks on the existence of multiple polyphase decompositions of a rational function. Such situations lead to restrictions on the use of polyphase IIR adaptive filters, in order to avoid slow convergence.

NLMS algorithm with decreasing step size for adaptive IIR filters

In this paper, we modify the GLMS algorithm to become the proposed LMS-SAS algorithm, which can more effectively converge to the global minimum of the mean-square output error (MSE) objective function. We also derive the infinite impulse response-normalized least-squares algorithm (IIR-NLMS), whose behavior is similar to the LMS-SAS algorithm. The GLMS algorithm achieves its global search capability by appending a random perturbing noise to the LMS algorithm. Similarly, we suggest that such perturbing noise is to be multiplied by its MSE objective function in the proposed LMS-SAS algorithm. For the NLMS algorithm, we use the gradient estimation error, which exists naturally in the adaptive process, to act as perturbing noise. We have shown, theoretically and experimentally, that the LMS-SAS and NLMS algorithm do converge to the global minimum.

Adaptive IIR filter design for single sensor applications

The goal of this research was to investigate the theoretical design and physical implementation of a digital adaptive IIR filter to serve as an enhancement to the traditional active RC or passive RLC anti-aliasing filter. This all-digital filter will reside directly on the DSP engine. As explained in the paper, the adaptive IIR filter is designed to process an oversampled signal coming from a single sensor to reject noise in an acquisition system. Differentiation between the noise and the signal is obtained by exploiting the different auto-correlation functions of the two signals. In contrast to oversampling techniques employed in sampled data systems that are designed to relax the requirements of an analog anti-aliasing filter, this filter will track a signal in the frequency domain. Several power spectral density plots are given to illustrate the performance of the new filter. The results also indicate that the new filter performs well as compared to the Wiener filter in the stationary case.

Blind intrinsically-stable 2-pole IIR filtering

A preliminary study is presented on intrinsically-stable discrete-time 2-pole IIR adaptive filtering for blind equalisation based on minimum-entropy deconvolution. Structural-adapting theory is developed and numerical experimental results are discussed which illustrate the soundness of the proposed theory: The adaptive filter maintains stability and good deconvolution results are obtained.

Continuous action reinforcement learning automata and their application to adaptive digital filter design

In the design of adaptive IIR filters, the multi-modal nature of the error surfaces can limit the use of gradient-based and other iterative search methods. Stochastic learning automata have previously been shown to have global optimisation properties making them suitable for the optimisation of filter coefficients. Continuous action reinforcement learning automata are presented as an extension to the standard automata which operate over discrete parameter sets. Global convergence is claimed, and demonstrations are carried out via a number of computer simulations.

Reply to "Comments on adaptive IIR filtering with monic normalization"

Kim and Song (see IEEE Signal Processing Lett., vol.6, p.35-37, 1999) focused on the bias removal capability of the monic normalization equation error (MNEE) algorithm and showed in another paper (see IEEE Signal Processing Lett., vol.7, p.54-56, 2000) that the parameter estimated by the MNEE algorithm converges to the solution of the well-known eigenvalue equation presented by Regalia (1994), which is based on the unit-norm constraint. However, the convergence properties of the MNEE have not been fully understood. Some of its convergence issues were commented upon by Soderstrom (see vol.48, p.892-94, 2000). In the MNEE, there is a small bias of order O(/spl mu/). Under a certain condition, the MNEE may not be convergent. In this reply to Soserstrom's comments, we provide some remarks related to the above issues.

Adaptive lattice IIR filtering revisited: convergence issues and new algorithms with improved stability properties

Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz-McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with properties are derived. They are based on the cascade lattice structure, which allows the derivation of sufficient conditions for local stability.

Recursive LMS L-filters for noise removal in images

The problem of designing the weights for recursive L-filters optimized by the least mean square (LMS) algorithm is addressed. The coefficients derived for nonrecursive filtering are not optimal for recursive implementation, where the estimate of current pixel depends on the past outputs of the filter. To combat this, analogous to the design of adaptive IIR filters, the optimization scheme referred to as equation-error formulation is employed. The recursive filter performs better in suppressing noise than its nonrecursive counterpart.

Adaptive IIR filter initialization via hybrid FIR/IIR adaptive filter combination

A novel hybrid adaptive FIR/IIR filter configuration is presented. The aim is to reduce the main obstacles limiting the use of adaptive IIR filters: namely convergence and stability. The hybrid scheme attempts to exploit the good qualities of both system adaptive FIR filters (good convergence and stability) and those for adaptive IIR filters (sharp transition bands, lower order, and complexity). In this paper, the hybrid scheme is presented for a system identification problem, and the task is achieved in three main steps: (a) A training signal is applied to an adaptive FIR filter to achieve a near optimum approximation; (b) the FIR coefficients are mapped through the balanced model reduction technique to a smaller set of coefficients initializing an adaptive IIR filter; (c) there is a process of fine tuning (small adaptive stepsize) the adaptive IIR coefficients for further approximation precision. The IIR filter in the hybrid scheme makes use of the Steiglitz McBride algorithm that assures the stability of the filter. Furthermore, the convergence to the minimum error performance is enforced by the fact that the adaptive IIR filter is operating close to the optimum, requiring very small pole perturbation. The hybrid scheme is compared against the adaptive IIR filter initialized with a set of zero coefficients.

Adaptive IIR filtering of nonstationary signals

This paper presents global stability of the adaptive IIR filter in a nonstationary environment. For the estimation of time-varying parameters, the normalized least-mean-square (LMS) algorithm based on the output error method is used. We assume the presence of a possibly colored and nonstationary measurement noise. The global stability analysis is carried out in a deterministic context, and it is shown that the filter output is uniformly bounded for all initial conditions. We then consider the special case when the noise is a martingale difference sequence, and establish the almost sure mean-square performance in a stochastic framework.

On orthogonal realizations for adaptive IIR filters

Convergence speed is one of the main concerns in adaptive IIR filters. Fast convergence can be closely related to adaptive filter realization. However, with the exception of the lattice realization that is based on the nice properties of Szëgo orthonormal polynomials, no other adaptive IIR filter realization using orthonormal characteristics seems to be extensively studied in the literature. Furthermore, many orthogonal realizations for adaptive FIR filters, that are particularly suitable for rational modelling, have been proposed in the past years. Since rational orthogonal basis functions are a powerful tool for efficient system representation they seem attractive for adaptive IIR filters. In this paper, we present some theoretical results related to the properties of a generalized orthonormal realization when used for mean-square output error minimization in a system identification application. One result is related to the low computational complexity of the updating gradient algorithm when some properties of the orthonormal realization are used. An additional result establishes conditions for the stationary points of the proposed updating algorithm. In order to confirm the expected performance of the new realization, some simulations and comparisons with competing realizations in terms of computational complexity and convergence speed are presented. Copyright © 2000 John Wiley & Sons, Ltd.