**Next:** Introduction

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).

**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 ...*

** **

Mon Nov 13 10:51:25 EST 1995