Since two decades, wavelet packet decompositions have been shown effective as a generic approach to feature extraction from time series and images for the prediction of a target variable. Redundancies exist between the wavelet coefficients and between the energy features that are derived from the wavelet coefficients. We assess these redundancies in wavelet packet decompositions by means of the...

The main objective of this course is to conduct a study on wavelet theory from both theoretical and application perspective (such as signal compression, denoising, communication systems, and recognition) in a coherence manner. The course first builds up background on LTI operators and Fourier analysis (including Shannon’s sampling theory) and its short comings. Windowed Fourier Transform (WFT) ...

AbstmctIn our previous work, we showed empirically that independent wavelet models were parsimonious, computationally efficient, and accurate in modeling heterogeneous network traffic measured by both auto-covariance functions and buffer loss rate. In this work, we focus on auto-covariance functions, to establish a theory of independent wavelet models as unified models for heterogeneous network...

We introduce a framework for calculating sparse approximations to signals based on elements of continuous wavelet systems. The method is based on an extension of the continuous wavelet theory. In the new theory, the signal space is embedded in larger abstract signal space, which we call the window-signal space. There is a canonical extension of the wavelet transform on the window-signal space, ...

the aim of this paper is a) if σak2 < ∞ then σak rk(x) is in bmo that{rk(x)} is rademacher system. b) p1k=1 ak!nk (x) 2 bmo; 2k  nk < 2k+1that f!n(x)g is walsh system. c) if jakj < 1k then p1k=1 ak!k(x) 2 bmo.

New adaptive search methods based on multiresolution analysis and wavelet theory are introduced and discussed within the framework of Markov theory. These stochastic search methods are suited to problems for which good solutions tend to cluster within the search space. Multiresolution search methods are extended to searches with memory. The introduction of a memory allows an easy inclusion of l...

In order to have fault identification for the gate rotor shaft with multiple cracks effectively, the quantity identification method of the gate rotor shaft with multiple cracks based on wavelet finite element method is established and the frequency test of the gate rotor shaft based on blind source separation algorithm is analyzed. Firstly the wavelet finite element was established by combining...

The problem of wavelet synthesis is a crucial part of wavelet theory. In this paper an overview of wavelet synthesis methods used in the literature up till now is given. It is demonstrated that these well known approaches suffer from some major drawbacks. A new approach to adaptive wavelet synthesis that overcomes these drawbacks and has not been exploited before is proposed. This approach is b...