Adaptive Infinite Impulse Response Filters Research Articles

A novel and efficient algorithm for adaptive filtering: Artificial bee colony algorithm

The uni-modal error surfaces and intrinsic stable behaviors of adaptive finite impulse response (FIR) filters make gradient based algorithms very effective in the design of these filters. Gradient based design methods are well developed for the design of adaptive FIR filters and widely applied to the distinct areas such as noise cancellation, system identification and channel equalization. However, the studies on adaptive infinite impulse response (IIR) filters are not as common as adaptive FIR filters since the stability during the adaptation process may not be ensured in some applications, and the convergence to the optimal design is not always guaranteed due to their multi-modal error surface structures. Gradient based design approaches may often get stuck at a local minimum in a multi-modal error surface and the stability of the designed filter can not be ensured. However, global optimization algorithms based approaches are able to converge to the global minimum in a multi-modal error surface and ensure the stability of the adaptive IIR filter. One of the most recently proposed swarm intelligence based global optimization algorithms is the artificial bee colony algorithm, which simulates the intelligent foraging behavior of honeybee swarms. In this work, a novel approach based on artificial bee colony algorithm is introduced for the design of adaptive FIR and adaptive IIR filters. Simulations are realized for the noise cancellation problem and the performance of the proposed approach is compared to that of some known gradient and evolutionary based approaches.

Novel adaptive IIR filter for frequency estimation and tracking [DSP Tips&Tricks

In many applications, a sinusoidal signal may be subjected to nonlinear effects in which possible harmonic frequency components are generated. In such an environment, we may want to estimate (track) the signal's fundamental frequency as well as any harmonic frequencies. Using a secondorder notch filter to estimate fundamental and harmonic frequencies is insufficient since it only accommodates one frequency component. On the other hand, applying a higher-order infinite impulse response (IIR) notch filter may not be efficient due to adopting multiple adaptive filter coefficients. In this article, we present a novel adaptive harmonic IIR notch filter with a single adaptive coefficient to efficiently perform frequency estimation and tracking in a harmonic frequency environment. Furthermore, we devise a simple scheme to select the initial filter coefficient to insure algorithm convergence to its global minimum error.

IIR Filter Adaptation Using Branch-and-Bound: A Novel Approach

Adaptive infinite impulse response (IIR) filters provide significant advantages over equivalent finite impulse response (FIR) implementations because they are able to more accurately model physical plants that have pole-zero structures. Additionally, they are typically capable of meeting performance specifications using fewer filter parameters. This savings in parameters, which can be as much as 5-10 times, leads to the use of fewer multiplier blocks and therefore, lower power consumption. Despite these advantages, adaptive IIR filters have not found widespread use because the associated mean squared error (MSE) cost function is multimodal and therefore, significantly difficult to minimize. Additionally, the filter can become unstable during adaptation. These two properties pose several problems for adaptive algorithms, causing them to be sensitive to initial conditions, produce biased solutions, unstable filter configurations or converge to local minima. These problems prevent the widespread use of adaptive IIR filters in practice and if such filter structures are to become more practical, new, innovative solutions are required. This paper proposes a new algorithm for minimizing the MSE cost function of adaptive IIR filters aimed at addressing some of the aforementioned issues. We adopt the approach of using a branch-and-bound algorithm, which is an exhaustive search method, and employ interval arithmetic for all computations. Simulation results show that the resulting algorithm is viable and competitive and, when compared with a number of existing state-of-the-art algorithms, outperforms them in terms of the MSE of the final point.

A modified adaptive IIR filter design via wavelet networks based on Lyapunov stability theory

In this paper, we present a wavelet network IIR filtering system satisfying asymptotic stability in the sense of Lyapunov unlike many other gradient descent algorithms based adaptive filtering systems. The proposed system also carries the advantages of the time-frequency specific properties of wavelet networks embedded into the proposed filter dynamics. Two experiments for system identification problems corresponding to the infinite impulse response filter design are proposed. The results verified that the proposed wavelet network infinite impulse response adaptive filtering system not only performs better than gradient descent based algorithms but also performs as good as other stability theory based optimization algorithms.

Equation-Error Adaptive IIR Filtering Based on Data Reuse

An equation-error adaptive infinite-impulse response (IIR) filtering method has slow convergence rate when the input signal is correlated. To overcome this problem, we present a new equation-error adaptive IIR filtering method based on data reuse. We also provide the corresponding debiasing solution for the proposed algorithm. Experimental result demonstrates that the proposed algorithm has much faster convergence rate than the conventional one.

Adaptive IIR Filters for Single Interference Suppression in a BPSK DS CDMA System In Rayleigh Fading Channel

In this paper, effect of a single narrow-band interference (NBI) on bit error rate (BER) performance for a binary phase shift keying (BPSK) synchronous direct-sequence code-division multiple access (DS CDMA) communication system operating in a frequency nonselective Rayleigh fading channel is analyzed. Second-order adaptive infinite impulseresponse (IIR) notch filters with plain gradient algorithm (GA) for suppression of NBI in the DS CDMA system are proposed. A general closed-form BER expression for the DS CDMA system with NBI suppression second order adaptive IIR notch filters is derived based on the standard Gaussian approximation (SGA) method. BER expressions are then derived for the allpass filter-based adaptive IIR notch filter and adaptive IIR notch filter with constrained poles and zeros, the two structures that are commonly found in literature. It is observed that both adaptive IIR notch filter structures exhibit comparable BER performance. Extensive computer simulation results are presented to verify the accuracy and limitations of the analysis.

A new framework for convergence analysis and algorithm development of adaptive IIR filters

A parameterization of an adaptive infinite impulse response (IIR) filter's poles is developed, based on balanced realization theory. From this, we develop a local approximation of the actual adapted pole parameters, in which convergence speed is related to a certain eigenvalue spread. This, in turn, is shown to relate to the Hankel singular values of the system to be identified, as well as certain coefficient sensitivity functions of the adapted filter. The local approximation is not restricted to stationary points. At these points, however, it is equivalent to a Hessian approximation, with the benefit of decomposing the Hessian matrix into terms related to the aforementioned singular values and sensitivity functions. The description of the adaptation process by means of the developed approximation leads to a greater understanding of the effects on convergence speed of factors, such as the Hankel singular values of the system, its order, the distribution of its poles, and the choice of adapted parameters. In particular, the use of direct form and lattice parameters are compared in detail. Based on these properties, a new adaptive IIR algorithm with faster convergence and relatively low computational complexity has recently been proposed, which is briefly mentioned. Results also indicate a potential for variable gain algorithms.

Design and performance of adaptive systems based on structured stochastic optimization strategies

The theory and design of linear adaptive filters based on FIR filter structures is well developed and widely applied in practice. However, the same is not true for more general classes of adaptive systems such as linear infinite impulse response adaptive filters (MR) and nonlinear adaptive systems. This situation results because both linear IIR structures and nonlinear structures tend to produce multi-modal error surfaces for which stochastic gradient optimization strategies may fail to reach the global minimum. After briefly discussing the state of the art in linear adaptive filtering, the attention of this paper is turned to MR and nonlinear adaptive systems for potential use in echo cancellation, channel equalization, acoustic channel modeling, nonlinear prediction, and nonlinear system identification. Structured stochastic optimization algorithms that are effective on multimodal error surfaces are then introduced, with particular attention to the particle swarm optimization (PSO) technique. The PSO algorithm is demonstrated on some representative IIR and nonlinear filter structures, and both performance and computational complexity are analyzed for these types of nonlinear systems.

A new method for adaptive IIR filter design based on tabu search algorithm

Adaptive digital filters have proven their worth in a wide range of applications such as channel equalisation, noise reduction, echo cancelling, and system identification. These filters can be broadly classified into two groups: finite impulse–response (FIR) and infinite impulse–response (IIR) filters. IIR filters have become the target of increasing interest because these filters can reduce the filter order significantly as compared to FIR filters. Tabu search is a heuristic optimisation algorithm which has been originally developed for combinatorial optimisation problems. It simulates the general rules of intelligent problem solving and has the ability of discovering the global minima in a multi-modal search space. In this work, a novel method based on tabu search is described for the design of adaptive IIR filters.

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.

Pole-cancelation error adaptive IIR filtering

We present an adaptive infinite-impulse response (IIR) filtering structure that is based on a novel performance measure. The proposed adaptive IIR filter consists of two finite-impulse response (FIR) filters that are directly driven by a noise-free input signal. One adaptive filter inversely estimates the poles, and the other filter directly estimates the zeros of an unknown system. Since the filter structure consists of two FIR filters, the performance measure is unimodal, and thus no local minimum exists. The simulation results demonstrate that the proposed method can indeed produce unique unbiased parameter estimates in the presence of both white and colored noise.

QR-based TLS and mixed LS-TLS algorithms with applications to adaptive IIR filtering

The least squares (LS), total least squares (TLS), and mixed LS-TLS approaches are compared as to their properties and performance on several classical filtering problems. Mixed LS-TLS is introduced as a QR-decomposition-based algorithm for unbiased, equation error adaptive infinite impulse response (IIR) filtering. The algorithm is based on casting adaptive IIR filtering into a mixed LS-TLS framework. This formulation is shown to be equivalent to the minimization of the mean-square equation error subject to a unit norm constraint on the denominator parameter vector. An efficient implementation of the mixed LS-TLS solution is achieved through the use of back substitution and inverse iteration. Unbiasedness of the system parameter estimates is established for the mixed LS-TLS solution in the case of uncorrelated output noise, and the algorithm is shown to converge to this solution. LS, TLS, and mixed LS-TLS performance is then compared for the problems of echo cancellation, noise reduction, and frequency equalization.

Lattice form adaptive infinite impulse response filtering algorithm for active noise control.

In some situations of active noise control, infinite impulse response (IIR) filters are more suitable than finite impulse response (FIR) filters owing to the poles in the transfer function. A number of algorithms have been derived for applying IIR filters in active noise control; however, most of them use the direct form IIR filter structure, which faces the difficulties of checking stability and relatively slow convergence speed for noise composed of narrow-band components with large power disparity. To overcome these difficulties along with using the direct form IIR filters, a new adaptive algorithm is proposed in this paper, which uses and updates the lattice form adaptive IIR filter in an active noise control system. Full mathematical derivations of the proposed algorithm are presented, and the comparison between the proposed algorithm and the commonly used filtered-u LMS and filtered-v LMS algorithms shows the superiority of the proposed algorithm.

Data-Reusing Recurrent Neural Adaptive Filters

A class of data-reusing learning algorithms for real-time recurrent neural networks (RNNs) is analyzed. The analysis is undertaken for a general sigmoid nonlinear activation function of a neuron for the real time recurrent learning training algorithm. Error bounds and convergence conditions for such data-reusing algorithms are provided for both contractive and expansive activation functions. The analysis is undertaken for various configurations that are generalizations of a linear structure infinite impulse response adaptive filter.

Lyapunov-theory-based radial basis function networks for adaptive filtering

Two important convergence properties of Lyapunov-theory-based adaptive filtering (LAF) adaptive filters are first explored. The LAF finite impulse response and infinite impulse response adaptive filters are then realized using the radial basis function (RBF) neural networks (NNs). The proposed adaptive RBF neural filtering system possesses the distinctive properties of RBF NN and the LAF filtering system. Unlike many adaptive filtering schemes using gradient search techniques, a Lyapunov function of the error between the desired signal and the RBF NN output is first defined. By properly choosing the weights update law in the Lyapunov sense, the RBF filter output can asymptotically converge to the desired signal. The design is independent of the stochastic properties of the input disturbances and the stability is guaranteed by the Lyapunov stability theory. Simulation examples for nonlinear adaptive prediction of nonstationary signal and system identification are performed.

A polyphase IIR adaptive filter

A polyphase structure for infinite-impulse response (IIR) adaptive filtering is proposed and compared to the direct structure in terms of their reduced error surface. It is shown that the general shape of its surface can make the polyphase structure have higher convergence speed, alleviating the problem of convergence speed in IIR adaptive filters and allowing their computational complexity gain over finite-impulse response (FIR) adaptive filters to be exploited. Benefits regarding filter stability are also achieved with the polyphase structure. An example of a high-speed digital subscriber line (HDSL) application is presented, for which the polyphase structure attains a gain of up to 70 times in convergence speed over an IIR direct structure, leading to roughly the same convergence speed of a FIR structure but with only 12% of its computational complexity. The question of uniqueness of the stationary points of the proposed structure is also discussed. It is pointed out that for white input and sufficient modeling, all stationary points are global minima, a result which does not follow directly from an equivalent property of the direct structure.

Intrinsic stability-control method for recursive filters and neural networks

Linear recursive filters can be adapted on-line but with instability problems. Stability-control techniques exist, but they are either computationally expensive or nonrobust. For the nonlinear ease, e.g., locally recurrent neural networks, the stability of infinite-impulse response (IIR) synapses is often a condition to be satisfied. This brief considers the known reparametrization-for-stability method for the on-line adaptation of IIR adaptive filters. A new technique is also presented, based on the further adaptation of the squashing function, which allows one to improve the convergence performance. The proposed method can be applied to various filter realizations (direct forms, cascade or parallel second order sections, lattice form), as well as to locally recurrent neural networks, such as the IIR multi-layer perceptron (IIR-MLP), with improved performance with respect to other techniques and to the case of no stability control. In this brief, the case of normalized lattice filters is particularly considered; an analysis of the stabilization effects is also presented both analytically and experimentally.

Hyperspherical parametrization for unit-norm based adaptive IIR filtering

The bias problem associated with equation error based adaptive infinite impulse response (IIR) filtering can be surmounted by imposing a unit-norm constraint on the autoregressive (AR) coefficients. We propose a hyperspherical parameterization to convert the unit-norm-constrained optimization into an unconstrained optimization. We show that the hyperspherical parameterization does not introduce any additional minima to the equation error surface.

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.

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.