Hi all,
The short-time fourier transform decomposes a signal window into a sin/cosine series.
How would one approximate a signal in the same way, but using a set of arbitrary basis functions instead of sin/cos? These arbitrary basis functions are likely in my case to be very small discrete chunks of a 1-dimensional non-periodic waveform.
Is this something wavelets are used for?
Please excuse my tag, 'signal-analysis' does not exist and I can not create it.
Best Answer
Wavelets are generally used for nonperiodic signals. They're often used in earthquake detection and things like that. There are many books on the subject, a quick look for "Wavelets" in amazon.com should reveal many.
The Haar Wavelet and Daubchies Wavelet might be good choices. Haar may be better if you don't need a smooth decomposition, the wavelet decomposition their is much easier.
Google scholar (scholar.google.com) may be a good place to look, just look up "Wavelet decomposition" and your particular topic.
You can make your own wavelets per your particular needs, but it's not particularly easy, they need to fulfill certain conditions
This may be useful
https://doi.org/10.1007/BF01257191
Generalized multi-resolution analyses and a construction procedure for all wavelet sets in R^n
If you can get this down to 1-d you may have your answer.