Next: Introduction

Tutorial
on Continuous Wavelet Analysis
of Experimental Data

Jacques Lewalle, Syracuse University

April 1995.

The preparation of this document was supported in part by NASA-Dryden (TM: Martin Brenner) through Creare Inc (Drs. Miller and Magari).

Abstract:

Our purpose is to make the wavelet techniques approachable without unnecessary mathematical sophistication. Therefore, graphics are more important than the formulae or analytical results, shown in small print. Also, with the expectation that the user wants to interrogate his or her data from the viewpoint of the underlying physics, only a few simple wavelets with readily interpretable transforms are used: the first two Gaussians and the Morlet wavelets. The examples range from cosines to modulated and intermittent data.

I. Introduction

II. Basic tools

III. Enhancement and statistical reduction

IV. Further reading

 

Check here for related papers by this author.

• Introduction
• One example
• A wavelet
• Analysis of a cosine wave
• Continuous wavelet transforms
• Interpretation:
• Energy distribution
• Mean power spectrum
• Interpretation
• Frequency/duration relation.
• Analysis of a multiperiodic signal
• Transform of modulated oscillations
• Inverse transform
• Morlet wavelet and transform
• Morlet transform of modulated oscillations
• General formulae
• Commentary
• Feature enhancement: pulsing
• Feature enhancement: filtering and denoising
• Feature enhancement: normalizing
• Feature enhancement: local maxima
• Data reduction: histograms and pdf's
• Data reduction: moments, conditional sampling, etc
• Recommended reading
• I. Daubechies, 1992, 10 Lectures on Wavelets, S.I.A.M.
• Y. Meyer, 1993, Wavelets: Algorithms and Applications, S.I.A.M.
• About this document ...

 

Jacques Lewalle
Mon Nov 13 10:51:25 EST 1995