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I am working with DWT2 on matlab for a 2D matrix of time series data. When I perform dwt2 on the matrix, it returns the follwing four values :
[ca,ch, cv, cd] = dwt2(mat,'db4','mode', 'per')

I read about what these four values CA, CH, CV and CD represent in the link : Discrete Wavelet Transform Matlab

But I did not get, why does dwt2 down samples the given matrix or data by 2? And on what basis it performs the down sampling of the given data?

For example. In my matrix, rows = timestamp and column = attributes/features. After dwt2, it gives me the matrix of [(size row/2) by (column/2)]. The features are reduced from 8 to 4 and also the number of the timestamps in the original matrix is reduced by 2. So does this mean that dwt2 automatically determines the important attributes or features from the original matrix? Also can anyone briefly explain CA, CH, CV, CD as well?

Piyush Doke
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  • If you've read what the output values are, but still don't understand what they represent, then the explanation you read wasn't good enough. Maybe some more literature search would help. In short: It computes a *decomposition*, all information from the input is spread out over 4 matrices that each have 1/4 of the samples. These are meant for images, don't apply a wavelet decomposition to your feature table, I don't think that means anything. – Cris Luengo Jan 22 '19 at 20:44
  • @CrisLuengo Thanks. Can you suggest what would be better way to get the important features from the feature matrix. I have tried FFT for the same. And for the dwt, the given data in the feature matrix is a time series data. Would it still not be a good fit for wavelet decomposition? – Piyush Doke Jan 23 '19 at 07:31
  • A 1D wavelet transform of a time series could be meaningful, depending on how the sampling was performed. If you can treat the series as a single sampled signal, then yes. If each time point contains independent data, and you're trying to classify each time point, then no. -- But computing the decomposition across the "features" axis is meaningless. Don't use a 2D wavelet transform. – Cris Luengo Jan 23 '19 at 15:17

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