Adaptive Infinite Impulse Response Research Articles

A constrained transform domain adaptive IIR filter structure for active noise control

An active noise controller utilizing a transform domain recursive LMS (RLMS) infinite impulse response (IIR) filter is presented in this paper. The new filter, termed the TRLMS adaptive filter, mitigates the filter instability problems that often exist with controllers based on direct form IIR filters by directly constraining the adaptation of the filter's frequency response. A filtered-U adaptive algorithm for the TRLMS filter structure is derived. Two different implementations of the constrained TRLMS filter are discussed. The first represents the adaptive filter in terms of its transform domain weights. They are directly adapted by the filtered-U TRLMS adaptive algorithm. The second implementation represents the filter in terms of its original time domain weights. These are updated by the filtered-U RLMS algorithm and subsequently projected onto an adaptation subspace at each iteration. Extensions of these algorithms that enforce soft constraints on the filter response are also presented. The stability of the constrained TRLMS adaptive filter is investigated utilizing two different transformations.

Pipelined adaptive IIR filter architectures using scattered and relaxed look-ahead transformations

Fine-grain pipelined architectures for adaptive infinite impulse response (AIIR) filters are presented in this paper. The AIIR filters are equation error based. The proposed architectures are developed by employing a combination of scattered look-ahead and relaxed look-ahead pipelining techniques. First, a pipelined system identification scenario is developed. Then, the scattered look-ahead technique is applied to the nonadaptive (but time-varying) recursive section. Finally, a relaxed look-ahead technique is applied to the adaptive blocks. Convergence analysis of the pipelined architectures is presented and verified via simulations. It is shown that speedups of up to 8 and more can be achieved with marginal or no degradation in performance.

A novel type of 2-D cascade-parallel adaptive IIR filters

A new type of 2-D cascade-parallel adaptive infinite impulse response (IIR) filters with adaptive algorithm based on the concept of back propagation method is developed. This class of filter consists of parallel blocks each of which includes all-zero (transversal) and all-pole sections in cascade form realizations. At first a 2-D cascade-parallel filter structure is introduced, then an efficient adaptive algorithm is proposed using the concept of backpropagating the desired signal. Finally, the applications of this type of 2-D adaptive IIR filters in 2-D system identification and noise reduction in an image are illustrated with numerical examples.

APPLICATION OF FREQUENCY DOMAIN ADAPTIVE INFINITE IMPULSE RESPONSE FILTERING FOR IDENTIFICATION OF FLEXIBLE STRUCTURE DYNAMICS

The identification problem of transfer functions associated with flexible structures is addressed in this paper. An adaptive infinite impulse response filter with data preprocessing in the frequency domain is used to identify directly the poles of the transfer function and the coefficients of the numerator polynomial. The parallel form realisation is utilised to model the structure of the identified transfer function. The stability of the identified system can easily be monitored and the sensitivity of its coefficients is lower compared to that of the classical direct form. Simulation studies are used to illustrate the proposed algorithm.

A block gradient-based algorithm for adaptive IIR filtering

This paper presents a new block gradient-based adaptive algorithm for Infinite Impulse Response (IIR) adaptive filters. In contrast with the Recursive Prediction Error (RPE) algorithm, the proposed algorithm employs more accurate gradient estimates. The gradients are calculated based on sampled data blocks, within which the filter coefficients are kept constant. The proposed approach is characterised by improved steady-state performance and reduced computational complexity when compared with the conventional RPE algorithm.

Parallel adaptive infinite impulse response digital filters using Kalman filters

AbstractThis paper presents a new design method for parallel adaptive infinite impulse response (112) digital filters using Kalman filters in the time domain. the parallel Kalman filter (PKF) and the improved parallel Kalman filter (IPKF) based on the divided estimation of an unknown system's impulse response are extended to parallel adaptive IIR digital filters. the finite impulse response (FIR) digital filters can be replaced by reduced order IIR digital filters. This is particularly useful when high‐order FIR digital filters are necessary. A method is presented that ensures the stability of IIR digital filters with little extra computational effort.

Adaptive IIR filtering algorithms for system identification: a general framework

Adaptive IIR (infinite impulse response) filters are particularly beneficial in modeling real systems because they require lower computational complexity and can model sharp resonances more efficiently as compared to the FIR (finite impulse response) counterparts. Unfortunately, a number of drawbacks are associated with adaptive IIR filtering algorithms that have prevented their widespread use, such as: convergence to biased or local minimum solutions; requirement of stability monitoring; and slow convergence. Most of the recent research effort on this field is aimed at overcoming some of the above mentioned drawbacks. In this paper, a number of known adaptive IIR filtering algorithms are presented using a unifying framework that is useful to interrelate the algorithms and to derive their properties. Special attention is given to issues such as the motivation to derive each algorithm and the properties of the solution after convergence. Several computer simulations are included in order to verify the predicted performance of the algorithms. >

Tracking random walk systems with vector space adaptive filters

Tracking properties are considered for adaptive filters that are adjusted within a vector space of filtering operations. Such vector space adaptive filters have both the desirable convergence properties of adaptive finite impulse response filters, and additionally some of the modeling flexibility of adaptive infinite impulse response filters. For a given vector space of systems, the adaptive filter structure is determined by a choice of basis for the vector space. Basis dependent expressions are developed for the asymptotic mean square error under least mean square, recursive least square, and Kalman filtering adaptation, when the optimal filter specification is subject to random walk variations. It is shown that under these conditions, the minimum achievable mean square error using least mean square adaptation is equal to the optimal value provided by the Kalman filtering algorithm, but that recursive least squares adaptation does not in general attain this minimum error.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Power system harmonic signal estimation and retrieval for active power filter applications

This paper presents a new adaptive infinite impulse response (IIR) line enhancer (LE) comb filter configuration for the purpose of power system harmonic signal estimation and retrieval. The approximate maximum likelihood (AML) algorithm is employed for the parameter update. The proposed solution is characterised by modest computational burden, effective tracking capabilities and provides the retrieved harmonic components with little or no distortion. The retrieved power system harmonics may be obtained on an individual basis or as a composite signal. Practical test results are included which show the performance achieved by the proposed technique. >

Decision feedback equalization of HDSL using a generalized adaptive IIR delay filter

AbstractA decision feedback equalization scheme comprising of a generalized adaptive infinite impulse response delay filter in the feedback path is proposed and used for equalization of high‐rate digital subscriber loops including severe intersymbol interference and near‐end crosstalk colored noise. The feedback filter compensates the long postcursor intersymbol interference due to the high sampling rate and is composed of parallel sections having one, two or four coefficients and a delay element. The structures of the sections are determined adaptively and in a step‐by‐step procedure. Because of the parallel and, at most, two‐pole sections of the generalized adaptive infinite impulse response delay filter, the stability monitoring requires essentially no computations. To reduce the noise enhancement effect of the prefilter, an adaptive noise predictor is also used. Computer simulation results demonstrate the performance of the proposed structure compared to the conventional decision feedback equalizer with a finite impulse response feedback filter. The main advantage of the proposed system is the significant reduction in the number of coefficients and consequently the adaptation time.

Adaptive IIR comb filter for harmonic signal cancellation

A novel adaptive infinite impulse response (IIR) comb filter structure for the estimation and elimination of harmonic interference signals is presented. Two filter blocks are presented. The first is an adaptive notch filter implemented by a computationally simple but exact gradient-based algorithm. The adaptive notch filter is used to estimate and track the fundamental frequency of the harmonic series. The second block is a tunable IIR comb filter whose parameters are determined based on the estimate of the fundamental frequency. The purpose of both filter blocks is to effectively cancel the harmonic series. The proposed comb filtering is more robust as well as computationally simpler than the comb filtering technique used by Nehorai and Poraz (1986). Error surface analysis is included to indicate that the error surface characteristics for the proposed solution is a significant improvement when compared to the conventional adaptive comb filter approach used by Nehorai and Poraz (1986). Simulation results are included to demonstrate the performance characteristics of the proposed solution.

Multichannel active control of random noise in a small reverberant room

An algorithm for multichannel adaptive IIR (infinite impulse response) filtering is presented and applied to the active control of broadband random noise in a small reverberant room. Assuming complete knowledge of the primary noise, the theoretically optimal reductions of acoustic energy are initially calculated by means of a frequency-domain model. These results are contrasted with results of a causality constrained theoretical time-domain optimization which are then compared with experimental results, the latter two results showing good agreement. The experimental performances of adaptive multichannel FIR (finite impulse response) and IIR filters are then compared for a four-secondary-source, eight-error microphone active control system, and it is found that for the present application FIR filters are sufficient when the primary noise source is a loudspeaker. Some experiments are then presented with the primary noise field generated by a panel excited by a loudspeaker in an adjoining room. These results show that far better performances are provided by IIR and FIR filters when the primary source has a lightly damped dynamic behavior which the active controller must model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The gamma-filter-a new class of adaptive IIR filters with restricted feedback

Generalized feedforward filters, a class of adaptive filters that combines attractive properties of finite impulse response (FIR) filters with some of the power of infinite impulse response (IIR) filters, are described. A particular case, the gamma filter, generalizes Widrow's adaptive transversal filter (adaline) to an infinite impulse response filter. Yet, the stability condition for the gamma filter is trivial, and LMS adaptation is of the same computational complexity as the conventional transversal filter structure. Preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter. The authors extend the Wiener-Kopf equation to the gamma filter and develop some analysis tools. >

An Adaptive Lattice Architecture for Dynamic Multilayer Perceptrons

Time-series modeling is a topic of growing interest in neural network research. Various methods have been proposed for extending the nonlinear approximation capabilities to time-series modeling problems. A multilayer perceptron (MLP) with a global-feedforward local-recurrent structure was recently introduced as a new approach to modeling dynamic systems. The network uses adaptive infinite impulse response (IIR) synapses (it is thus termed an IIR MLP), and was shown to have good modeling performance. One problem with linear IIR filters is that the rate of convergence depends on the covariance matrix of the input data. This extends to the IIR MLP: it learns well for white input signals, but converges more slowly with nonwhite inputs. To solve this problem, the adaptive lattice multilayer perceptron (AL MLP), is introduced. The network structure performs Gram-Schmidt orthogonalization on the input data to each synapse. The method is based on the same principles as the Gram-Schmidt neural net proposed by Orfanidis (1990b), but instead of using a network layer for the orthogonalization, each synapse comprises an adaptive lattice filter. A learning algorithm is derived for the network that minimizes a mean square error criterion. Simulations are presented to show that the network architecture significantly improves the learning rate when correlated input signals are present.

An adaptive backpropagation cascade IIR filter

Among the various linear infinite impulse response (IIR) structures for adaptive filters, cascade IIR filters are notable for easy stability monitoring and good sensitivity performance. However, their high cost for computing gradients is a problem. A novel technique of backpropagating the desired signal is proposed, and a cascade structure satisfying the requirements of this technique is developed, resulting in an efficient adaptive IIR filter. It is shown that the equation-error formulation is just a special case of this backpropagation idea.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simplified gradient calculation in adaptive IIR lattice filters

A simplified algorithm is presented for computing the gradient in adaptive IIR (infinite impulse response) lattice filters. For a filter with N zeros and N poles, this algorithm requires only order N computations. Several computer simulations were performed to compare the performance of the proposed O(N) formulation and the conventional O(N/sup 2/) formulation, and no difference in their behavior was found. In these simulations the full Hessian and the diagonal Hessian adaptive algorithms were used in a system-identification configuration. It is concluded that the proposed method allows the development of robust adaptive IIR algorithms with a cost proportional to the filter order.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Efficient filter structures for active noise, LMS controllers

Two new controller configurations for broad band adaptive noise control have been examined. In the proposed structures, a certain amount of the properties of the acoustic system are modelled by a fixed part of the controller which is therefore less flexible than a completely adaptive control system. The benefit with these configurations are that the adaptive part can be small and can therefore obtain a higher efficiency in terms of attenuation per adaptive weight. It is assumed that the acoustic impulse response has a short term mean value that is stationary or almost stationary and that the variations are small around the mean value. The controller configurations presented here are general and the actual filter implementation may consist of finite impulse response (FIR) filters or infinite impulse response (IIR) filters as dictated by the properties of the acoustic system. The configurations discussed in this paper are especially useful in applications where long impulse responses are needed in order to obtain a high attenuation over a large bandwidth. Instead of using a completely adaptive IIR filter, the combination of a fixed part with a sufficiently long impulse response and a small adaptive part allows us to maintain the transversal controller structure and a very simple adaptive algorithm, such as the LMS algorithm, can be used to control the adaptive weights. Two realisations have been examined and compared with the ordinary transversal filter configuration in a computer simulation study. The results show that it is possible to obtain a significant reduction in the controller complexity if prior knowledge about the acoustic system is built into the controller.

An improved lattice-based adaptive IIR notch filter

A novel lattice-based adaptive infinite impulse response (IIR) notch filter is developed which features independent tuning of the notch frequency and attenuation bandwidth. The internal structure is based on planar rotators, ensuring reliable numerical behaviour and high processing rates in CORDIC environments. A simple update law allows a simpler implementation than previously proposed designs. Rather than minimizing an output error cost function, the algorithm is designed to achieve a stable associated differential equation, resulting in a globally convergent unbiased frequency estimator in the single sinusoid case, independent of the notch filter bandwidth. Using a second-order structure in the multiple sinusoid case, unbiased estimation of one of the input frequencies is achieved by thinning the notch bandwidth. The tracking behavior is superior to conventional output error designs, and the estimation of extremal frequencies is less prone to overflow instability than previously reported structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Derivation of an adaptive algorithm for IIR digital systems realized by power-wave digital filters

This paper presents a new efficient algorithm for adjusting the coefficients of an adaptive infinite impulse response power-wave digital filter in order to estimate the discrete-time signal y(k) as the recursively filtered version of the signalx(k). To do this, eight different prediction errors are defined which can be computed recursively with respect to model order and time, which leads to similar recursions as for the lattice algorithm [1], where autoregressive processes are considered. These recursions can be implemented as a digital filter which can be separated in ananalysis and asynthesis part, where the latter can be interpreted as a power-wave digital filter [2], [3], [13]. Hence, the stability of this adaptive network is always guaranteed [4]. Furthermore, it is shown that the proposed algorithm can be considered as an extension of the Levinson algorithm [7] for the efficient inversion of a special class of matrices.

Analysis of a frequency-domain adaptive IIR filter

Convergence of frequency-domain adaptive pole-zero IIR (infinite impulse response) filter is studied. The algorithm is shown to converge in probability to an associated ordinary differential equation (ODE) which in turn converges to a local minimum of its performance surface. An analysis of the performance surface shows that the algorithm converges to one of N-factorial members in an equivalence class of global minimum points, where N is the number of adaptive poles. Saddle points exist on manifolds that separate members in the equivalence class. This explains 'shoulders' in the MSE convergence curves and also suggests one way of avoiding these shoulders which cause slow convergence. A second-order simulation example confirms the above results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>