We study fractional Brownian motions in multifractal time, a model for multifractal processes proposed recently in the context of economics. Our interest focuses on the statistical properties of the wavelet decomposition of these processes, such as residual correlations (LRD) and stationarity, which are instrumental towards computing the statistics of wavelet-based estimators of the multifracta...

We study the problem of estimating the log spectrum of a stationary Gaussian time series by thresholding the empirical wavelet coe cients. We propose the use of thresholds t j;n depending on sample size n, wavelet basis and resolution level j. At ne resolution levels (j= 1; 2; :::), we propose

The continuous wavelet transform may be enhanced by deconvolution with the wavelet response function. After correcting for the coneof-influence, the power spectral density of the solar magnetic record as given by the derectified yearly sunspot number is calculated, revealing a spectrum of odd harmonics of the fundamental Hale cycle, and the integrated instant power is compared to a reconstructi...

The analysis of electrical signals is a pressing requirement for the optimal design of power distribution. In this context, this paper illustrates how to use a variety of numerical tools, such as the Fourier, wavelet, and Hilbert-Huang transforms, to obtain information relating to the active and reactive power absorbed by different types of users. In particular, the Fourier spectrum gives the m...

The method of speaker recognition based on wavelet functions and neural networks is presented in this paper. The wavelet functions are used to obtain the approximation function and the details of the speaker’s averaged spectrum in order to extract speaker’s voice characteristics from the frequency spectrum. The approximation function and the details are then used as input data for decision-maki...

In this paper, we consider the data mining problem of gene selection based on expression data and propose a method based on wavelet power spectrum. Wavelet power spectrum of the data has been analyzed and on the basis of the observations, a parameter was defined and used to select the features. Our proposed method has been applied on three types of cancer datasets. The results are in comparable...

A good watermarking scheme should be able to perform equally well on all types of images irrespective of image contents because practically watermarking has to be applied to images of all types. In this paper, it is shown that in wavelet based spread spectrum technique, watermarking at level 1 decomposition is better for textured images while watermarking at level 2 decomposition is better for ...

Gabor deconvolution has been updated and a new ProMAX module is released. The updates are: (1) a new method of spectral smoothing called hyperbolic smoothing; (2) a Gabor transform using compactly supported windows that improves run times by one to two orders of magnitude; and (3) a post-deconvolution time-variant bandpass filter whose maximum frequency tracks along a hyperbola in the time-freq...

Abstract We present the results of a wavelet-based approach to the study of the chaotic dynamics of a one-dimensional model that shows a direct transition to spatiotemporal chaos. We find that the dynamics of this model in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wave number). A projection onto a Daubechies basis yields a good...

It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet spectrum of a locally stationary wavelet time series. Our new method works by combining the advantages of a Haar-Fisz transformed spectrum with a simple, but po...