The continuous wavelet transform is employed to analyze the dynamics and time-dependent energy distribution of phonon wave-packet propagation and scattering in molecular dynamics simulations. The equations of the one-dimensional continuous wavelet transform are presented and then discretized for implementation. Practical aspects and limitations of the transform are discussed, with attention to ...

This paper concerns the issue of wavelet analysis of signals by continuous and discrete wavelet transforms (CWT – Continous Wavelet Transform, DWT – Discrete Wavelet Transform). The main goal of our work was to develop a program which, through the CWT and the DWT analyses, would obtain graph of time-scale changes and would transform it into the spectrum, that is a graph of frequency changes. In...

In this paper we present an algorithm for optical phase evaluation based on the wavelet transform technique. The main advantage of this method is that it requires only one fringe pattern. This algorithm is based on the use of a sًecond /2 phase shifted fringe pattern where it is calculated via the Hilbert transform. To test its validity, the algorithm was used to demodulate a simulated fringe p...

The information extraction capability of two widely used signal processing tools, Hilbert Transform (HT) and Wavelet Transform (WT), is investigated to develop a multi-class fault diagnosis scheme for induction motor using radial vibration signals. The vibration signals are associated with unique predominant frequency components and instantaneous amplitudes depending on the motor condition. Usi...

A signal-based pattern-recognition approach is used for structural damage diagnosis with a single or limited number of input/output signals. The approach is based on extraction of the features of the structural response that present a unique pattern for each specific damage case. In this study, frequency-based features and time-frequency-based features were extracted from measured vibration sig...

The S transform, which is introduced in this correspondence, is an extension of the ideas of the continuous wavelet transform (CWT), and is based on a moving and scalable localizing Gaussian window. It is shown here to have some desirable characteristics that are absent in the continuous wavelet transform. The S transform is unique in that it provides frequency-dependent resolution while mainta...

We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on R. 2000 ...