A question about Wavelet transforms

[billano786]

Can anyone answer this?

In any introductory course to wavelets one finds a statement that wavelets are localised in both time and frequency hence one can find not only the frequency but also the time at which this frequency was present.

Applying wavelet transform to a set of data results in wavelet coifficients from these wavelet coifficients how do we infer this information about both time and frequency?

 

[me2please]

I assume you have d/l Mallat's "a wavelet tour of signal processing" book already.

Just take a look at the time frequency boxes of wavelet basis on page 10, 11 and 12. Each of these depicts the time-frequency relationship of different wavelet basis. The coef's from wavelet transform represent (pretty much the same as Fourier transform) the portions of the signal expanded into each of the basis --- in other words, the portion of the signal distributed into each time-frequency box.

Of if you have Vetterli's "wavelets and subband coding", look at fig. 1.8 page 8. It shows time-frequency box for wavelets, STFT, and Fourier.

 

[billano786]

May be I have not been able convey what I wanted to know. I wish to know whether it is possible to know from wavelet analysis whether a time series is periodic or chaotic??

Any ideas??

 

[me2please]

I have some questions. Normally, to solve a problem ones pick tools that fit.
Here are the questions:
1. If the objective is to detect whether the signal is periodic or not, why not using Fourier?
2. Since wavelets capture local characteristics of a signal, can any local feature be used to indentify a chaotic signal? Usually, a chaotic signal is characterized by "long term unpredictable", which means observing a signal for a short period might not be able to tell whether it is chaotic or not.

I guess you are doing the ECG analysis for arrhythmic detection--if not you can find more information from publications on that subject.

 

[billano786]

First let me thank you for showing intrest in this discussion.

I use standard pioncare section technique (surface of section plot) to find chaotic time series but it fails in 3D case.

 

[me2please]

Please explain what you mean by "fail".
Do you mean you apply Poincare map on trajectory of a dynamical system, but it fail to produce the map similar to those in the book?

or you mean you apply Poincare map to an arbitrary time series?