When applied to identification of time-varying systems, such as rapidly fading telecommunication channels, adaptive estimation algorithms built on the local basis function (LBF) principle yield excellent tracking performance but are computationally demanding. The subsequently proposed fast LBF (fLBF) algorithms, based on the preestimation principle, allow a substantial reduction in the complexity without significant performance losses. We propose a novel preestimator, called bidirectional, which further improves performance of the fLBF scheme.

We consider the problem of identification of communication channels with a mix of static and time-varying parameters. Such scenarios are typical, among others, in underwater acoustics. In this paper, we further develop adaptive algorithms built on the local basis function (LBF) principle resulting in excellent performance when identifying time-varying systems. The main drawback of an LBF algorithm is its high complexity. The subsequently proposed fast LBF (fLBF) algorithms, based on the preestimation principle, allow a significant reduction in the complexity for recursively computable basis functions, such as the complex exponentials. We propose a debiased fLBF algorithm which exploits the fact that only a part of the system parameters are time-varying. We also propose an adaptive technique to identify whether a particular tap is static or time-varying.

We consider identification of sparse linear systems with a mix of static and time-varying parameters. Such systems are typical in underwater acoustics (UWA), for instance, in applications requiring identification of the acoustic channel, such as UWA communications, navigation and continuous-wave sonar. The recently proposed fast local basis function (fLBF) algorithm provides high performance when identifying time-varying systems. In this paper, we further improve the performance of the fLBF algorithm by exploiting properties of the system. Specifically, we propose an adaptive time-invariance test to identify whether a particular system tap is static or time-varying and exploit this knowledge for choosing the number of basis functions. We also propose a regularization scheme that exploits the system sparsity and an adaptive technique for estimating the regularization parameter. Finally, a debiasing technique is proposed to reduce an inherent bias of fLBF estimates. The high performance of the fLBF algorithm with the proposed techniques is demonstrated in scenarios of UWA communications, using numerical and real experiments.

Two recursive least-squares (RLS) adaptive filtering algorithms are most often used in practice, the exponential and sliding (rectangular) window RLS algorithms. This popularity is mainly due to existence of low-complexity versions of these algorithms. However, these two windows are not always the best choice for identification of fast time-varying systems, when the identification performance is most important. In this paper, we show how RLS algorithms with arbitrary finite-length windows can be implemented at a complexity comparable to that of exponential and sliding window RLS algorithms. Then, as an example, we show an improvement in the performance when using the proposed finite-window RLS algorithm with the Hanning window for identification of fast time-varying systems.

The problem of identification of a nonstationary autoregressive process with unknown, and possibly time-varying, rate of parameter changes, is considered and solved using the parallel estimation approach. The proposed two-stage estimation scheme, which combines the local estimation approach with the basis function one, offers both quantitative and qualitative improvements compared with the currently used single-stage methods.

In this paper the problem of detection of impulsive disturbances in archive audio signals is considered. It is shown that semi-causal/noncausal solutions based on joint evaluation of signal prediction errors and leave-one-out signal interpolation errors, allow one to noticeably improve detection results compared to the prediction-only based solutions. The proposed approaches are evaluated on a set of clean audio signals contaminated with real click waveforms extracted from silent parts of old gramophone recordings.

When estimating the correlation/spectral structure of a locally stationary process, one should choose the so-called estimation bandwidth, related to the effective width of the local analysis window. The choice should comply with the degree of signal nonstationarity. Too small bandwidth may result in an excessive estimation bias, while too large bandwidth may cause excessive estimation variance. The paper presents a novel method of adaptive bandwidth selection. The proposed approach is based on minimization of the cross-validatory performance measure for a local vector autoregressive signal model and, unlike the currently available methods, does not require assignment of any user-dependent decision thresholds.

The problem of active feedback control of a narrowband acoustic noise in the presence of impulsive disturbances is considered. It is shown that, when integrated with appropriately designed outlier detector, the proposed earlier feedback control algorithm called SONIC is capable of isolating and rejecting noise pulses. According to our tests this guarantees stable and reliable operation of the closed-loop noise cancelling system.

This paper presents a new approach to elimination of impulsive disturbances from stereo audio recordings. The proposed solution is based on vector autoregressive modeling of audio signals. Online tracking of signal model parameters is performed using the exponentially weighted least squares algorithm. Detection of noise pulses and model-based interpolation of the irrevocably distorted samples is realized using an adaptive, variable-order Kalman filter. The proposed approach is evaluated on a set of clean audio signals contaminated with real click waveforms extracted from old gramophone recordings.

The paper presents a new approach to detection of apnea/hypopnea events, in the presence of artifacts and breathing irregularities, from a single-channel airflow record. The proposed algorithm, based on a robust envelope detector, identifies segments of signal affected by a high amplitude modulation corresponding to apnea/hypopnea events. It is shown that a robust airflow envelope-free of breathing artifacts-improves effectiveness of the diagnostic process and allows one to localize the beginning and the end of each episode more accurately. The performance of the proposed approach, evaluated on 30 overnight polysomnographic recordings, was assessed using diagnostic measures such as accuracy, sensitivity, specificity, and Cohen's coefficient of agreement; the achieved levels were equal to 95%, 90%, 96%, and 0.82, respectively. The results suggest that the algorithm may be implemented successfully in portable monitoring devices, as well as in software-packages used in sleep laboratories for automated evaluation of sleep apnea/hypopnea syndrome.

The problem of elimination of impulsive disturbances from archive audio signals is considered and its new solution, called predictive matched filtering, is proposed. The new approach is based on the observation that a large percentage of noise pulses corrupting archive audio recordings have highly repetitive shapes that match several typical “patterns”, called click templates. To localize noise pulses, click templates can be correlated with the sequence of multi-step-ahead prediction errors yielded by the model-based signal predictor. It is shown that predictive matched filtering is an efficient and computationally affordable disturbance localization technique - when combined with the classical detection method based on autoregressive modeling, it can significantly improve restoration results.

The paper presents a new approach to elimination of broadband noise and impulsive disturbances from archive audio recordings. The proposed adaptive Kalman-like algorithm, based on a sparse autoregressive model of the audio signal, simultaneously detects noise pulses, interpolates the irrevocably distorted samples and performs signal smoothing. It is shown that bidirectional (forward-backward) processing of the archive signal improves smoothing efficiency and allows one to localize noise pulses more accurately, leading to noticeable performance improvements compared to unidirectional processing.

A new adaptive comb filtering algorithm, capable of tracking the fundamental frequency and amplitudes of different frequency components of a nonstationary harmonic signal embedded in white measurement noise, is proposed. Frequency tracking characteristics of the new scheme are studied analytically, proving (under Gaussian assumptions and optimal tuning) its statistical efficiency for quasi-linear frequency changes. Laboratory tests show that the proposed algorithm can be successfully used for active control of MRI noise.

In this application-oriented paper we consider the problem of elimination of impulsive disturbances, such as clicks, pops and record scratches, from archive audio recordings. The proposed approach is based on bidirectional processing-noise pulses are localized by combining the results of forward-time and backward-time signal analysis. Based on the results of specially designed empirical tests (rather than on the results of theoretical analysis), incorporating real audio files corrupted by real impulsive disturbances, we work out a set of local, case-dependent fusion rules that can be used to combine forward and backward detection alarms. This allows us to localize noise pulses more accurately and more reliably, yielding noticeable performance improvements, compared to the traditional methods, based on unidirectional processing. The proposed approach is carefully validated using both artificially corrupted audio files and real archive gramophone recordings.

In this paper we suggest how several competing image denoising algorithms, differing in design parameters, or even in design principles, can be combined together to yield a better and more reliable denoising algorithm. The proposed fusion mechanism allows one to combine practically all kinds of noise reduction tools. It also allows one to account for the distribution of measurement noise, and in particular - to cope with heavy-tailed disturbances, such as Laplacian noise, or light-tailed disturbances, such as uniform noise.

The problem of estimation of the slowly-varying instantaneous frequency of a nonstationary complex sinusoidal signal buried in noise is considered. This problem is usually solved using frequency tracking algorithms. It is shown that the accuracy of frequency estimates can be considerably in creased if the results yielded by the frequency tracker are further processed using the appropriately designed filters. The resulting frequency smoother can be employed in many off-line applications. Whenever signal frequency varies in a sufficiently smooth manner, the proposed algorithm, based on a new, quasi-linear model of frequency changes, outperforms the existing solutions.

This paper presents a new approach to rejection of sinusoidal disturbances acting at the output of a discrete-time complex-valued linear stable plant (e.g. acoustic channel) with unknown and possibly time-varying dynamics. It is assumed that the instantaneous frequency of the sinusoidal disturbance may be slowly varying with time and that the output signal is contaminated with wideband measurement noise. It is not assumed that a reference signal, correlated with the disturbance, is available. The proposed disturbance rejection algorithm automatically adjusts its adaptation gains to the rate of system and/or disturbance variation.

The problem of extraction/elimination of nonstationary sinusoidal signals from noisy measurements is considered. This problem is usually solved using adaptive notch filtering (ANF) algorithms. It is shown that the accuracy of frequency estimates can be significantly increased if the results obtained from ANF are backward-time filtered by an appropriately designed lowpass filter. The resulting adaptive notch smoothing (ANS) algorithm can be employed to perform many off-line signal processing tasks, such as elimination of sinusoidal interference from a prerecorded signal. In the single sinusoid case, we show that when the unknown signal frequency drifts according to the random-walk model, the optimally tuned ANS algorithm is, under Gaussian assumptions, statistically efficient, i.e., it attains the Cramer-Rao type lower smoothing bound, which limits accuracy of any frequency estimation scheme.

It is shown that estimation accuracy of adaptive notch filters (ANFs) can be increased by combining two techniques that were previously used separately: automatic gain adjustment and frequency debiasing. To achieve this goal one has to solve a nontrivial problem of determining estimation delay introduced by a variable-gain ANF filter.

Generalized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. It is shown that frequency biases, which arise in generalized adaptive notch filtering algorithms, can be significantly reduced by incorporating in the adaptive loop an appropriately chosen decision delay. The resulting performance gains can be substantial. The proposed method can be used both in the system case and in the signal case.

The problem of identification/tracking of quasi-periodically varying systems is considered. This problem is a generalization, to the system case, of a classical signal processing task of either elimination or extraction of nonstationary sinusoidal signals buried in noise. The proposed solution is based on the exponentially weighted basis function (EWBF) approach. First, the global EWBF algorithm is derived and its decomposed, parallel-form and cascade-form variants, are described. Then the frequency-adaptive versions of both schemes are obtained using the recursive prediction error method. In the (special) signal processing case the paper offers new attractive solutions to the problem of adaptive notch filtering.

When system parameters vary rapidly with time the weighted least squares filters are not capable of following the changes satisfactorily-some more elaborate estimation schemes, based on the method of basis functions, have to be used instead. The basis functions estimators have increased tracking capabilities but are computationally very demanding. The paper introduces a new class of adaptive filters, based on the concept of postfiltering, which have improved parameter tracking capabilities, typical of the basis functions algorithms, but, at the same time, have pretty low computational requirements, typical of the weighted least squares algorithms.