Victor E. DeBrunner

Efficient Adaptive Nonlinear Filters for Nonlinear Active Noise Control

In this paper, we treat nonlinear active noise control (NANC) with a linear secondary path (LSP) and with a nonlinear secondary path (NSP) in a unified structure by introducing a new virtual secondary path filter concept and using a general function expansion nonlinear filter. We discover that using the filtered-error structure results in greatly reducing the computational complexity of NANC. As a result, we extend the available filtered-error-based algorithms to solve NANC/LSP problems and, furthermore, develop our adjoint filtered-error-based algorithms for NANC/NSP. This family of algorithms is computationally efficient and possesses a simple structure. We also find that the computational complexity of NANC/NSP can be reduced even more using block-oriented nonlinear models, such as the Wiener, Hammerstein, or linear-nonlinear-linear (LNL) models for the NSP. Finally, we use the statistical properties of the virtual secondary path and the robustness of our proposed methods to further reduce the computational complexity and simplify the implementation structure of NANC/NSP when the NSP satisfies certain conditions. Computational complexity and simulation results are given to confirm the efficiency and effectiveness of all of our proposed methods

A New Active Noise Control Algorithm That Requires No Secondary Path Identification Based on the SPR Property

Active noise control (ANC) has been widely applied in industry to reduce environmental noise and equipment vibrations. Most available control algorithms require the identification of the secondary path, which increases the control system complexity, contributes to an increased residual noise power, and can even cause the control system to fail if the identified secondary path is not sufficiently close to the actual path. In this paper, based on the geometric analysis and the strict positive real (SPR) property of the filtered-x LMS algorithm, we introduce a new ANC algorithm suitable for single-tone noises as well as some specific narrowband noises that does not require the identification of the secondary path, though its convergence can be very slow in some special cases. We are able to extend the developed ANC algorithm to the case of active control of broadband noises through our use of a subband implementation of the ANC algorithm. Compared to other available control algorithms that do not require secondary path identification, our developed method is simple to implement, yields good performance, and converges quickly. Simulation results confirm the effectiveness of our proposed algorithm

Multiscale storm identification and forecast

We describe a recently developed hierarchical K-Means clustering method for weather images that can be employed to identify storms at different scales. We describe an error-minimization technique to identify movement between successive frames of a sequence and we show that we can use the K-Means clusters as the minimization template. A Kalman filter is used to provide smooth estimates of velocity at a pixel through time. Using this technique in combination with the K-Means clusters, we can identify storm motion at different scales and choose different scales to forecast based on the time scale of interest. The motion estimator has been applied both to reflectivity data obtained from the National Weather Service Radar (WSR-88D) and to cloud-top infrared temperatures obtained from GOES satellites. We demonstrate results on both these sensors.

Resolution in time-frequency

We introduce a new measure H/sub p/ that is related to the Heisenberg uncertainty principle. The measure predicts the compactness of discrete-time signal descriptions in the sample-frequency phase plane. We conjecture a lower limit on the compaction in the phase plane and show that discretized Gaussians may not provide the most compact basis.

A novel adaptive nonlinear predistorter based on the direct learning algorithm

The nonlinear predistorter is an effective technique to compensate the nonlinear distortions existing in a digital communication system. However, available adaptive nonlinear predistorters are either based on the indirect learning algorithm, or are complicated in structure and computation. In this paper, we propose a novel adaptive nonlinear predistorter based on a direct learning algorithm: the adjoint nonlinear LMS algorithm. Because of the direct learning algorithm, our adaptive predistorter outperforms the other nonlinear predistorters that are based on the indirect learning method in the sense of mean square error (MSE). Moreover, compared with any other adaptive nonlinear predistorter based on the direct learning architecture, our predistorter has a simpler structure and lower computational complexity. Simulation results show the effectiveness of our nonlinear adaptive predistorter.

The optimal transform for the discrete Hirschman uncertainty principle

We determine all signals giving equality for the discrete Hirschman uncertainty principle. We single out the case where the entropies of the time signal and its Fourier transform are equal. These signals (up to scalar multiples) form an orthonormal basis giving an orthogonal transform that optimally packs a finite-duration discrete-time signal. The transform may be computed via a fast algorithm due to its relationship to the discrete Fourier transform.

Multiple fully adaptive notch filter design based on allpass sections

We develop a canonical, adaptive cascade-structure IIR notch filter to detect and track multiple time-varying frequencies in additive white Gaussian noise. The algorithm uses allpass frequency transformation filters and a truncated gradient. Simulations indicate that our algorithm is computationally simple, converges rapidly, and has good frequency resolution.

Hybrid filtered error LMS algorithm: another alternative to filtered-x LMS

The filtered-error LMS (FELMS) algorithms are widely used in multi-input and multi-output control (MIMO) active noise control (ANC) systems as an alternative to the filtered-x LMS (FXLMS) algorithms to reduce the computational complexity and memory requirements. However, the available FELMS algorithms introduce significant delays in updating the adaptive filter coefficients that slow the convergence rate. In this paper, we introduce a novel algorithm called the hybrid filtered-error LMS algorithm (HFELMS) which, while still a form of the FELMS algorithm, allows users to have some freedom to construct the error filter that guarantees its convergence with a sufficiently small step size. Without increasing the computational complexity, the proposed algorithm can improve the control system performance in one of several ways: 1) increasing the convergence rate without extra computation cost; 2) reducing the remaining noise mean square error (MSE); or 3) shaping the excess noise power. Simulation results show the effectiveness of the proposed method

On the Design of Sparse Half-Band Like FIR Filters

In this work we consider the design of sparse FIR filters, i.e. filters with few non-zero multiplications. The considered filters have half-band like properties, but with slightly relaxed specifications compared with actual half-band filters. We propose a filter design technique where the number of non-zero filter coefficients is minimized. It is shown by examples that it is possible to take advantage of an increased passband ripple only to obtain a half-band like solution with fewer non-zero multiplications. Decreasing the passband edge only does not give such a direct improvement.

Error control and concealment for image transmission

In the practical transmission of compressed still images, bit errors may occur, which probably result in desynchronization and packet loss. In packet-switched networks, network congestion also results in packet loss. This survey article reviews the error resilience factors that must be faced by a robust image encoder and decoder (codec). The article begins with the enumeration of the different kinds of impact noisy channels and congested networks have on block-coded images. Then we present different techniques that can be applied to combat the degradation of the images introduced by the noisy channel and network congestion. These techniques include resynchronization strategies, post-processing error concealment algorithms, and preprocessing error control techniques. All these techniques can be either used directly or extended to robust video transmission.