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This paper presents the concept of Intrinsic Wavelet Functions (IWFs) for efficient analysis of signals with transitory behavior. An approach is proposed for the decomposition of a given signal, consisting of localized waves, into IWFs that can best capture these small waves. To this end, first, we present a method to design a 2-channel signal-matched wavelet system based on least squares criterion...
This paper presents a new approach for the estimation of 2-channel nonseparable wavelets matched to images in the statistical sense. To estimate a matched wavelet system, first, we estimate the analysis wavelet filter of a 2-channel nonseparable filterbank using the minimum mean square error (MMSE) criterion. The MMSE criterion requires statistical characterization of the given image. Because wavelet...
In this paper, we present the characterization of the discrete-time fractional Brownian motion (dfBm). Since, these processes are non-stationary; the auto-covariance matrix is a function of time. It is observed that the eigenvalues of the auto-covariance matrix of a dfBm are dependent on the Hurst exponent characterizing this process. Only one eigenvalue of this auto-covariance matrix depends on time...
This paper presents a novel variable step-size LMS (VSLMS) algorithm for tracking a discrete-time fractional Brownian motion that is inherently non-stationary. In the proposed work, one of the step-size values requires time-varying constraints for the algorithm to converge to the optimal weights whereas the constraints on the remaining step-size values are time-invariant in the decoupled weight vector...
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