An overview is presented of several methods, filter structures, and recursive algorithms used in adaptive infinite-impulse response (IIR) filtering. Both the equation-error and output-error formulations are described, although the focus is on the adaptive algorithms and properties of the output-error configuration. These parameter-update algorithms have the same generic form, and they are based on a prediction-error performance criterion. A direct-form implementation of the adaptive filters is emphasized, but alternative realizations such as the parallel and lattice forms are briefly discussed. Several important issues associated with adaptive IIR filtering, including stability monitoring, the SPR condition, and convergence, are addressed. >

Adaptive IIR filtering

In this paper, an adaptive notch filter is developed (employing a frequency domain and time domain analysis) for the enhancement and tracking of sinusoids in additive noise, colored or white. The notch filter is implemented as a constrained infinite impulse response filter with the constraint enforced by a single parameter termed the debiasing parameter. The resulting notch filter requires few parameters, facilitates the formation of the desired band rejection filter response, and also leads to various useful implementations (cascade, parallel). For the adaptation of the filter coefficients, the stochastic Gauss-Newton algorithm is used. The convergence of this updating procedure is established by studying the associated differential equation. Also, it is shown that the structure present in the problem enables truncation of the gradient, thereby reducing the complexity of adapting the filter coefficients. Simulation results are presented to substantiate the analysis, and to demonstrate the potential of the notch filtering technique.

Adaptive notch filtering for the retrieval of sinusoids in noise

A tutorial-style framework is presented for understanding the current status of adaptive infinite-impulse-response (IIR) filters The paper begins with a detailed discussion of the difference equation models that are useful as adaptive IIR filters The particular form of the resulting prediction error generic to adaptive IIR filters is highlighted and the structures of provable convergent adaptive algorithms are derived A brief summary of particular, currently known performance properties, drawn principally from the system identification literature, is followed by the formulation of three illustrative adaptive signal processing problems, to which these adaptive IIR filters are applicable The concluding section discusses various open issues raised by the formulation of this framework

Adaptive IIR filtering: Current results and open issues

The use of infinite impulse response (IIR) adaptive filters has lagged behind that of finite impulse response (FIR) adaptive filters. This has been due, in part, to the increased complexity of IIR filters and the potential for instability that exists due to the presence of poles in the transfer function. This paper discusses the use of adaptive filters for the active cancellation of acoustic noise. It is shown that IIR filters possess certain characteristics that are highly desirable for this problem. The selection of an appropriate IIR adaptive algorithm is discussed using observability considerations. It is shown that the recursive least mean square (RLMS) algorithm of Feintuch possesses significant advantages for use in a practical active attentuation system. Results are presented from computer simulations as well as an actual system using a TI TMS32010 digital signal processing microprocessor.

The selection and application of an IIR adaptive filter for use in active sound attenuation

The concept of adaptation in digital filtering has proven to be a powerful and versatile means of signal processing in applications where precise a priori filter design is impractical. Adaptive filters have traditionally been implemented with FIR structures, making their analysis fairly straightforward but leading to high computation cost in many cases of practical interest (e.g, sinusoid enhancement). This paper introduces a class of adaptive algorithms designed for use with IIR digital filters which offer a much reduced computational load for basically the same performance. These algorithms have their basis in the theory of hyperstability, a concept historically associated with the analysis of closed-loop nonlinear time-varying control systems. Exploiting this theory yields HARF, a hyperstable adaptive recursive filtering algorithm which has provable convergence properties. A simplified version of the algorithm, called SHARF, is then developed which retains provable convergence at low convergence rates and is well suited to real-time applications. In this paper both HARF and SHARF are described and some background into the meaning and utility of hyperstability is given, in addition, computer simulations are presented for two practical applications of IIR adaptive filters: noise and multi-path cancellation.

P.L. Feintuch

Papers

Comments on and additions to "An adaptive recursive LMS filter"