Thomas Weickert

Analytic Wavelet Packets—Combining the Dual-Tree Approach With Wavelet Packets for Signal Analysis and Filtering

Real wavelets (or real basis functions in general) suffer from two major disadvantages: shift-variance and oscillating coefficients. This paper provides a review of these problems as well as the undecimated wavelet transform which solves the problem of shift-variance. However, undecimated transforms have very high computational costs and still have oscillating coefficients. The work of Kingsbury is summarized afterwards. They have presented a dual-tree complex wavelet transform (DTCWT) which is nearly shift-invariant and has smooth coefficients. Subsequently, a filter swapping scheme is developed in order to create complex wavelet packets with analytic basis functions. Finally, the effectiveness of the proposed method is demonstrated by five examples.

Analytic complex wavelet packets for speech enhancement

In previous work, the authors found the lack of shift invariance of real wavelet packets very disadvantageous for speech enhancement in the case of periodic noise. Therefore, this paper investigates the positive properties of the dual-tree complex wavelet transform (DTCWT). This transform is nearly shift invariant at moderate additional computational cost. However, the straightforward approach of extending the DTCWT to wavelet packets by decomposing the high pass coefficients as well led to non-analytic basis functions. Because analytic basis functions were required for the desired properties, a filter swapping scheme was developed to preserve analyticity. This analytic complex wavelet packet transform showed improved denoising performance for the application of speech enhancement and promises improvements for other applications like general filtering and signal analysis.

ADAPTIVE ESTIMATION OF PERIODIC NOISE ENERGY DISTRIBUTIONS FOR SPEECH ENHANCEMENT

Abstract Speech Enhancement aims at denoising a noisy speech signal and to extract the clean speech. In this work, nonstationary periodic noise is regarded. The coefficient energy distribution of a period of noise is analyzed by a Period Wavelet Packet transform. This transform can analyze signals of arbitrary (non-dyadic) length. The estimated coefficient energy distribution can be used as a threshold for wavelet thresholding techniques. The efficiency of the algorithm and its sensitivity to period variations is evaluated.

Application of a Sigma-point Kalman-filter for the Online Estimation of Fractional Order Impedance Models for Solid Oxide Fuel Cells

To operate a solid oxide fuel cell (SOFC) safely and efficiently, it is necessary to monitor the values of characteristic model parameters of the cell impedance. This paper addresses the problem to compute online estimates of model parameters for SOFCs, whose impedance is represented by a fractional (non-integer) order impedance model. The fractional model of the impedance is approximated through serial connection of a finite number of RC-elements. Assuming that the time-dependent model parameters of the impedance are treated as state-variables of an augmented state vector, the linearity is lost, and the application of the classical linear Kalman filter for state estimation is not longer possible. The so-called sigma-point Kalman filter is therefore used to solve the online estimation problem for nonlinear system dynamics. The feasibility and quality of this online identification approach is outlined using simulated data with additional noise.

APPLICATION OF A SIGMA-POINT KALMAN-FILTER FOR THE ONLINE ESTIMATION OF FRACTIONAL ORDER IMPEDANCE MODELS FOR SOLID OXIDE FUEL CELLS

Abstract To operate a solid oxide fuel cell (SOFC) safely and efficiently, it is necessary to monitor the values of characteristic model parameters of the cell impedance. This paper addresses the problem to compute online-estimates of model parameters for SOFCs, whose impedance is represented by a fractional (non-integer) order impedance model. The fractional model of the impedance is approximated by a serial connection of a finite number of RC-elements. Assuming that the time-dependent model parameters of the impedance are treated as state-variables of an augmented state vector, the linearity-property is lost and the application of the classical linear Kalman-filter for state estimation is not longer possible. Hence, the so-called sigma-point Kalman-filter is used in order to solve this online estimation problem for nonlinear system dynamics. The feasibility and quality of this online identification approach is outlined by using simulated data with additional noise.