How can we compute the correlation coefficient if the original signals(s) are significantly positively correlated with the approximation coefficient series (a1, a2, a3, a4, a5) in the wavelet decomposition and reconstruction of a specific signal?
Try
1. Reconstruct signal s with ai and di = ri
2 Do correlation of s with each ri.
3 or correlation only with ai and s
Cheers
Narasim Ramesh Thank you for your kind response. As far as I know, the length of the original signal s is not equal to di or ai since they are reduced by a factor of 2 in each consecutive level. Is it still possible to calculate the correlation? As I am learning to use this tool, please share some tutorials if you have any. It would be a great help to me.
Wavelet multiresolution analysis (MRA) consists of decomposing the time series into different scales of variations using the wavelet transform. A time series x(t) is decomposed into detail and smooth coefficients using the father (φ) and the mother (ψ) wavelets, respectively. The mother wavelet gives the detail coefficients (high-frequency components) and the smooth coefficient (low-frequency component) is computed at the highest multiresolution level J using the father wavelet.
It is just like a auto correlation of signal. You can verify it by CWT instead of DWT. The CWT function is available in MATLAB. The length of coefficients are equal in all decomposition levels. It is redundant wavelet decomposition or CWT.
Karunesh K. Gupta Thank you for your response. But, I am a bit unfamiliar to calculate the correlation coefficient in CWT, sir. While running the code, we normally get a) time series plot b)Wavelet Power Spectrum c) Global wavelet Spectrum d)Scale average variance. In that case, from where we get the information of the correlation coefficients?
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