Wavelets and High-frequency data
High Frequency, Signal Processing, Wavelet Transform February 17th. 2008, 11:49pmThis presentation covers almost everything I have been wanting to convey about the usefulness of wavelets.
The researchers propose a prototype feature extraction system, the block diagram of which is reproduced below:
Questions I ask:
- It appears that the researchers settled for a fixed wavelet function for doing the decomposition. Are there any benefits in using a hybrid of different wavelet families for decomposing different parts of the time series?
- Is it possible to create a custom wavelet family with the aim that it works better than the other wavelet families commonly used? What should be the line of approach to this kind of problem? Inductive or Deductive?
I am tempted to write a Matlab model to replicate this system and maybe adapt it a little bit, but there is a paper written by the researchers that needs to be understood first. You can download it from here.
March 8th, 2008 at 11:20 pm
Very nice info. I just like to add that the comparison between the wavelet method described above and the neural network that’s made on the paper, it’s not the best comparison the author could have made. He uses a simple feed-forward neural network topology with input time delays which limits the memory of the network to the number of delays. Instead of that, a much better comparison would be Wavelet Method vs. Recurrent Neural Network, as the recurrent topology propagates the network memory through time with no defined time limit. As a good example, you can compare the following, FIR vs. IIR filters and Feed-Forward vs. Recurrent Neural Networks.
By the way, this is a great site, i’ve just found it and im really glad i did. Thanks for all the great interesting posts!