This paper systematically studies the well-known Mexican hat wavelet (MHW) on manifold geometry, including its derivation, properties, transforms, and applications. The MHW is rigorously derived from the heat kernel by taking the negative first-order derivative with respect to time. As a solution to the heat equation, it has a clear initial condition: the Laplace–Beltrami operator. Following a ...

| We consider the problem of characterizing the lithology of a reservoir using gamma ray logs as well as seismic traces around the well. We rst calculate the continuous wavelet transform of the the data and then use the fact that the energy of such transformation is proportional to a power of its scale. The technique consists in estimating the power transformation obtaining a set of values of t...

This paper is concerned with the group-theoretical background of integral transforms and the role they play in signal processing on the sphere. An overview of topological groups, measure and representation theories, and an overview of the Windowed Fourier Transform and the Continuous Wavelet Transform are presented. A group-theoretical framework within which these transforms arise is presented....

introduction: studying long-term trend changes of meteorological parameters is one of the routine methods in atmospheric studies, especially in the climate change subject. among the meteorological parameters, temperature is always considered as one of the most atmospheric elements and studying it in order to gain a better understanding of the climate change phenomenon, has been effective. in ad...

This paper reports the study of four time-frequency transforms applied to vibration signals and presents a new metric for comparing them for fault detection. The four methods to be described and compared are the Short Time Frequency Transform (STFT), the Choi-Williams Distribution (WV-CW), the Continuous Wavelet Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel g...

With progress in radar systems, a number of methods have been developed for signal processing and detection in radars. A number of modern radar signal processing methods use time-frequency transforms, especially the wavelet transform (WT) which is a well-known linear transform. The interference canceling is one of the most important applications of the wavelet transform. In Ad-hoc detection met...

Fourier Transform and its tools have been applied popularly in many engineering applications. However, the Fourier Transform cannot analyze non-stationary, non-linear and intermittent signals with simultaneously time-frequency plane. Wavelet Transform have been invented recently to cope with limitations of the Fourier Transforms. This paper presents Continuous Wavelet Transform and its recent a...