Peter M. Clarkson

A class of order statistic LMS algorithms

Conventional gradient-based adaptive filters, as typified by the well-known LMS algorithm, use an instantaneous estimate of the error-surface gradient to update the filter coefficients. Such a strategy leaves the algorithm extremely vulnerable to impulsive interference. A class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented. These algorithms, dubbed order statistic least mean squares (OSLMS), are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from Gaussian to highly impulsive. Three specific OSLMS filters are defined: the median LMS, the average LMS, and the trimmed-mean LMS. The properties of these algorithms are investigated and the potential for improvement demonstrated. Finally, a general adaptive OSLMS scheme in which the nature of the order-statistic operator is also adapted in response to the statistics of the input signal is presented. It is shown that this can facilitate performance gains over a wide range of input data types. >

Envelope expansion methods for speech enhancement.

The last decade has seen increasing interest in techniques for the enhancement of digital speech signals. Significant gains have been made in terms of signal-to-noise ratio (SNR) and quality, but few techniques have produced improvements in intelligibility. A method for speech enhancement based on nonlinear expansion of the spectral envelope is presented. The expansion is consistent with both the long-term spectrum of the speech and with the probability that speech is present in a given sample. Objective SNR measures are used to compare this algorithm with the well-known spectral subtraction method, with an alternative expansion scheme, and with limiting SNRs resulting from perfect recovery of the amplitude spectrum. For the purpose of intelligibility assessments, a simplified version of the algorithm has been implemented on a Texas Instruments TMS320-C25 system. Listening trials with this real-time system, conducted using a modified rhyme test, have produced small, but consistent, improvements in articulation scores.

Performance characteristics of the median LMS adaptive filter

The median least-mean-square (MLMS) adaptive filter alleviates the problem of degradation of performance when inputs are corrupted by impulsive noise by protecting the filter coefficients from the impact of the impulses. MLMS is obtained from the least mean square (LMS) by applying a median operation to the raw gradient estimates of the mean-squared-error performance surface. The algorithm is analyzed for the class of independent and identically distributed inputs, establishing exponential convergence. The rate of convergence is shown to depend on order statistics of the input but shows little dependence on characteristics of the impulsive interference. Analysis of the steady-state performance indicates a significantly improved performance for MLMS compared to LMS. Analytic predictions for both convergence and steady-state behavior are supported by simulations. >

Reconstruction of speech signals with lost samples

A simple nonlinear system which can be implemented in real-time on a low-cost microprocessor system is proposed for recovering a speech signal from the remaining samples. It is shown that significant improvement can be obtained relative to simple interpolation schemes. Subjective tests verify the theoretical and objective simulation results. >

On the performance of a second-order adaptive Volterra filter

The impact of the bias or DC term on the performance of a second-order Volterra least-mean-square (LMS) filter is discussed. Without the DC term the filter may itself produce a biased output. It is shown that including a DC term always degrades adaptive system performance, in terms of both convergence and steady state. Unlike the usual LMS approach, the second-order scheme converges nonuniformly, even with white inputs. For deterministic signals an approximate transfer function descriptor is obtained for the second-order LMS filter. Jury (1964) tables are used to obtain explicit stability conditions. >

On signal recovery with adaptive order statistic filters

Adaptive order statistic filters are used to estimate a constant amplitude signal embedded in noise with unknown statistics. Iterative algorithms are proposed which adapt the order statistic filter to minimize the mean-square estimation error, both with and without an unbiasedness constraint. For each case, the algorithm used is shown to achieve convergence in the mean to the optimal filter. Properties of the convergence rates are discussed, and conditions for convergence in mean square are noted. >

Adaptive algorithms for non-Gaussian noise environments: the order statistic least mean square algorithms

Convergence properties are studied for a class of gradient-based adaptive filters known as order statistic least mean square (OSLMS) algorithms. These algorithms apply an order statistic filtering operation to the gradient estimate of the standard least mean square (LMS) algorithm. The order statistic operation in OSLMS algorithms can reduce the variance of the gradient estimate (relative to LMS) when operating in non-Gaussian noise environments. A consequence is that in steady state, the excess mean square error can be reduced. It is shown that when the input signals are iid and symmetrically distributed, the coefficient estimates for the OSLMS algorithms converge on average to a small area around their optimal values. Simulations provide supporting evidence for algorithm convergence. As a measurement of performance, the mean squared coefficient error of OSLMS algorithms has been evaluated under a range of noise distributions and OS operators. Guidelines for selection of the OS operator are presented based on the expected noise environment. >

The performance of adaptive noise cancellation systems in reverberant rooms

The performance of adaptive noise cancellation (ANC) systems in a reverberant room is investigated. Room reverberation effects are modeled through the method of images, incorporating both direct signal and reverberation effects into the room impulse response. The performance of ANC for broadband inputs is examined as a function of reverberation time, noise source location, and the geometry of the room and measurement equipment. Expressions are obtained relating the steady‐state minimum mean‐squared error and excess mean‐squared error to the reverberation time and filter parameters. Nonuniform convergence effects are also investigated and bounds on the eigenvalue disparity are obtained for a given configuration. It is shown that the eigenvalue disparity increases as both the filter length and the distance between noise source and reference receiver increase, approaching a limiting value as the distance from source to reference receiver surpasses the acoustic critical distance.

Analysis and generalization of a median adaptive filter

A class of gradient based adaptive algorithms is presented which employs order-statistical transformations of the gradient estimates over a short window. These algorithms, called order-statistical least mean squares (OSLMS), are designed to facilitate adaptive filter performance close to the least-squares optimum in impulsive and other non-Gaussian input environments. Three specific OSLMS filters are defined: the median LMS, the averaged LMS, and the trimmed-mean LMS. For the median LMS some simple convergence results are given. Simulations of all three algorithms, conducted using a generalized exponential density, are presented.<<ETX>>

On convergence and steady state behavior in the median LMS adaptive filter

The authors examine the performance of the MLMS (median least mean square) adaptive filter subjected to zero-mean independent, identically distributed inputs corrupted by sparse impulsive interference. They demonstrate exponential convergence in the mean to the minimum mean squared error solution. They find approximations for the convergence rates corresponding to different impulsive conditions and compare these to LMS. It is shown that, in contrast to LMS, MLMS enjoys smooth exponential convergence largely unaffected by the impulses. They also compare the impact of a single impulse on MLMS and LMS when the algorithms are operating in steady state. A reduced performance cost for MLMS, measured by the mean deviation of the filter coefficients from the optimal values, is demonstrated.<<ETX>>