Understanding Wavelet Transform for Time Series Data Analysis

[DavidLiew]

I have a time series data, I want to use wavelet transform to de-noise the data and then use neural network to analysis the transform data. However, I quite not understand about the wavelet transform. Can tell me about how to use wavelet transform? How to determine the scale? Is it suitable use the coefficients as a input to neural network for analysis?

 

[real10]

I have a time series data, I want to use wavelet transform to de-noise the data and then use neural network to analysis the transform data. However, I quite not understand about the wavelet transform. Can tell me about how to use wavelet transform? How to determine the scale? Is it suitable use the coefficients as a input to neural network for analysis?

MATLAB is your best bet to play around with the wavelet transform (i think they even have a toolbox)
-IEEE access and do some digging on the transforms (esp if someone used the output of them as the input to a neural network simulation) and how others have applied it..

I used the wavelet transform coefficients (daubechies) for an undergrad signal detection project...
depends on the input data (ours looked like the letter N (gunshots) with noise on it) the type and level of decomposition needed would vary (of course computational horsepower as well more levels would be slow basically u are splitting the signal by sending it thru low pass and bp filters and looking at it more closely...)
We kinda did a Normalized cross correlation (NCC) on the wavelet coefficients (incoming signal versus our database signature) and used some statistical estimation to classify when they would match (detecting the high peaks generated due to NCC)
The Wiki page is free :) (compared to IEEE and others) http://en.wikipedia.org/wiki/Daubechies_wavelet

 

[totinen]

You can also use R-language
http://en.wikipedia.org/wiki/R_(programming_language)

with Wavelet packet
http://cran.r-project.org/web/packages/wavelets/index.html

Good starter book about wavelets with R language
http://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-75960-9

 

[DavidLiew]

I now using MATLAB to analysis the data with discrete wavelet transform, but I don't know how to choose the best level for decomposition and what type of wavelet to use. Have any method to determine the level and wavelet? Besides, how to choose the suitable thresholding method and noise structure?

 

[totinen]

Maybe this would help you?
http://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf

And yes, you can use cofficients or sums of cofficients as a input data. You could use also a wavelet network where neurons activation functions are wavelet functions. See:
http://maths.york.ac.uk/www/sites/default/files/Veitch.pdf