Wavelets are of wide potential use in statistical contexts. The basics of the discrete wavelet transform are reviewed using a lter notation that is useful subsequently in the paper. A `stationary wavelet transform', where the coeecient sequences are not decimated at each stage, is described. Two diierent approaches to the construction of an inverse of the stationary wavelet transform are set ou...

Current methods for power spectrum estimation by wavelet thresholding use the empirical wavelet coefficients derived from the log periodogram. Unfortunately, the periodogram is a very poor estimate when the true spectrum has a high dynamic range and/or is rapidly varying. Also, because the distribution of the log periodogram is markedly non-Gaussian, special waveletdependent thresholding scheme...

We propose a robust method for estimating the time-varying spectrum of a non-stationary random process. Our approach extends Thomson's powerful multiple window spectrum estimation scheme to the time-frequency and timescale planes. The method reenes previous extensions of Thomson's method through optimally concentrated window and wavelet functions and a statistical test for extracting chirping l...

In this paper, we introduce a Goodness-of-Fit test for the Multivariate Exponential Power (MEP) distribution, a multivariate extension of the Generalized Gaussian, which has recently gained considerable interest as a model for wavelet coefficients in the context of color image retrieval and spread-spectrum watermarking. We present a size and power study of this test and show Goodness-of-Fit res...

This paper develops a new crop mapping method through combined utilization of both time and frequency information based on wavelet variance and Jeffries-Matusita (JM) distance (CIWJ for short). A two-dimensional wavelet spectrum was obtained from datasets of daily continuous vegetation indices through a continuous wavelet transform using the Mexican hat and the Morlet mother wavelets. The time-...

The purpose of this study was to identify the formation interfaces from geophysical well log data using the wavelet transform, and a combination of the wavelet transform and the Fourier transform methods. In the wavelet transform method, the identification of formation interfaces is based on the wavelet coefficients from the wavelet transform of spontaneous potential (SP) log and gamma ray (GR)...

one of the most fundamental reservoir characteristics is the thickness. the analysis of thin bed tuning on seismic reflectivity has been studied extensively by wides (1973) and neidel and pogiaggliomi (1977), who discussed the limits of seismic resolution. during the past decade, the industry has developed a plethora of new attributes in studying thin beds by employing spectral decomposition (p...

PURPOSE The wavelet transform is a newly developed signal-processing tool that decomposes a signal into various levels of resolution. The wavelet transform based noise reduction has the characteristics of optimally separating signal from noise, preserving the rapid rises and falls of a signal, and reconstructing a smooth signal from noise-imposed observations. The aim of this study was to evalu...

For cognitive radio networks, there is a major spectrum sensing problem, i.e. dynamic spectrum management. It is an important issue to sense and identify the spectrum holes in cognitive radio networks. The first-order derivative scheme is usually used to detect the edge of the spectrum. In this paper, a novel spectrum sensing technique for cognitive radio is presented. The proposed algorithm of...

Purpose of this work is to generalize the wavelet-transform modulus maxima method case cooperative dynamics interacting systems and introduce joint singularity spectrum into consideration. The research wavelet-based multifractal formalism, generalized version which used quantitatively describe effect chaotic synchronization in model systems. Models coupled Rossler paired nephrons are considered...