In this article we study function estimation via wavelet shrinkage for data with long-range dependence. We propose a fractional Gaussian noise model to approximate nonparametric regression with long-range dependence and establish asymp-totics for minimax risks. Because of long-range dependence, the minimax risk and the minimax linear risk converge to zero at rates that diier from those for data...

Generalizing the result of Bownik and Speegle [Approximation Theory X: Wavelets, Splines and Applications, Vanderbilt University Press, pp. 63–85, 2002], we provide plenty of non-MSF A-wavelets with the help of a given A-wavelet set. Further, by showing that the dimension function of the non-MSF A-wavelet constructed through an A-wavelet set W coincides with the dimension function of W , we con...

At present, much more soft sensing have been widely used in industrial process control to improve the quality of product and assure safety in production. A novel method using Hilbert-Huang transform (HHT) combined with wavelet support vector machine (WSVM) is put forward. Firstly the method analyzes the intrinsic mode function (IMF) obtained after the empirical mode decomposition (EMD), then ex...

In this paper, we present a direct solution method based on wavelet networks for image compression. Wavelet networks are a combination of radial basis function (RBF) networks and wavelet decomposition, where radial basis functions were replaced by wavelets. The results show that the wavelet networks approach succeeded to improve high performances in terms of compression ratio and reconstruction...

We consider the wavelet transform of a finite, rooted, node-ranked, p-way tree, focusing on the case of binary (p = 2) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through translation and dilation of a wavelet function. We explore how this works in our tree context.

For many natural signals, the wavelet transform is a more effective tool than the Fourier transform. The wavelet transform provides a multi resolution representation using a set of analyzing functions that are dilations and translations of a few functions. The wavelet transform lacks the shift-invariance property, and in multiple dimensions it does a poor job of distinguishing orientations, whi...

The identification of dynamic parameters is of prime importance in vibration analysis. A number of different time and frequency domain methods have been developed for vibration analysis of time-invariant systems. However, many engineering systems exhibit timevariant behavior. This paper presents a simulation example of a time-variant approach used for parameter identification in a simple vibrat...

Abstract We compare the capability of wavelet functions used for noise removal in preprocessing step of a QRS detection algorithm in the electrocardiogram (ECG) signal. The QRS signal to noise ratio enhancement and the detection accuracy of each wavelet function are evaluated using three measures: (1) the ratio of the maximum beat amplitude to the minimum beat amplitude (RMM), (2) the mean of a...

This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet connectivity problem.

Computation in the analog domain is very appealing from a power-consumption perspective. To implement a wavelet transform in an analog circuit, the wavelet function can be approximated by a linear system. An approach based on L2-approximation is presented, that enables largely automated approximation of wavelet functions by impulse responses of linear systems. Various continuous wavelet functio...