This paper is concerned with the definition of the discrete fractional Fourier transform (DFRFT). First, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions which are eigenfunctions of the continuous Fourier transform and by performing a novel error removal procedure. Then, the result of the eigendecomposition of the DFT matrix...

It is known that the Continuous Wavelet Transform of a distribution f decays rapidly near the points where f is smooth, while it decays slowly near the irregular points. This property allows the identification of the singular support of f . However, the Continuous Wavelet Transform is unable to describe the geometry of the set of singularities of f and, in particular, identify the wavefront set...

The analysis of 3D discrete volumetric data becomes increasingly important as computation power increases. 3D analysis and visualization applications are expected to be especially relevant in areas like medical imaging and nondestructive testing, where elaborated continuous theory exists. However, this theory is not directly applicable to discrete datasets. Therefore, we have to establish theor...

The paper illustrates a procedure based on the continuous-wavelet transform (CWT) for the analysis of current transients due to line faults. Considering roundly reliability and accuracy of one terminal fault location system for transmission lines, a single-ended continuous wavelet Transform (CWT) based fault location algorithm has been presented in this paper. Wavelet transform is a powerful ma...

Continuous and Discrete Wavelet Transform (WT) are used to create text-dependent robust to noise speaker recognition system. In this paper we investigate the accuracy of identification the speaker identity in nonstationary signals. Three methods are used to extract the essential speaker features based on Continuous, Discrete Wavelet Transform and Power Spectrum Density (PSD). To have better ide...

This paper presents a computational algorithm for identifying power frequency variations and integer harmonics by using waveletbased transform. The continuous wavelet transform (CWT) using the complex Morlet wavelet (CMW) is adopted to detect the harmonics presented in a power signal. A frequency detection algorithm is developed from the wavelet scalogram and ridges. A necessary condition is es...

A time scale is any closed subset of the real line. Continuous time and discrete time are special cases. The unilateral Laplace transform of a signal on a time scale subsumes the continuous-time unilateral Laplace transform, and the discretetime unilateral z-transform as special cases. The regions of convergence (ROCs) time scale Laplace transforms are determined by the time scale’s graininess....

Several algorithms are reviewed for computing various types of wavelet transforms: the Mallat algorithm, the “a trous” algorithm and their generalizations by Shensa. The goal is 1) to develop guidelines for implementing discrete and continuous wavelet transforms efficiently, 2) to compare the various algorithms obtained and give an idea of possible gains by providing operation counts. The compu...