What wavelet basis to choose?-more specifically-

Hi everyone,

I know you may have heard this question several times and the answer always is " it depends on the characteristics of your data and the application". But can you be more specific?

In wavelet toolbox user guide it has been written that " If you understand the properties of the analysis and synthesis wavelet, you can choose a wavelet that is optimized for your application." Can any of you give more detailed information?

I am trying to model a time series ( which resembles a sine wave, but not a perfect one)with wavelets.based on my limited knowledge, if I want better time resolution, I should use a shorter (compactly supported)wavelet and if I want good frequency resolution, I should use more regular ( smooth)ones. But honestly I don't know how to figure out which one is my case. I also know that wavelets with more vanishing moments result in sparser representations...and lastly, that the wavelet should look like the data...

I really appreciate it if you could give me some practical directions on how to find an optimized wavelet basis for my data.

Thank you for your support

Answer 1

[Star Strider]

When in doubt, experiment. For sinusoidal and physiological signals, I usually start with a Mexican Hat wavelet, then compare it with a Daubechies wavelet, and go from there. Wavelets have the ability to give you information about the signal you may not have realised existed, so this is somewhat heuristic, as is the choice between continuous and discrete.