Interpreting the results of DWT

Hi, I am currently using the DWT to detect transients in my signal. When doing the DWT on my signal I use the following command:

[cA,cD] = dwt(signal,'db4')

And when I plot cD and cA respectively, they both look like the original signal. Does this mean that there are both low and high frequency components in the dwt or is there another interpretation of this result?

[Jonas]

please provide your data signal such that we can have a look =)

[Alex]

This is an example of how my signal looks like. I expected the detail coefficients to consist of peaks in the beginning due to expected transient behavior in the beginning of my original signal.

Answer 1

[Dheeraj]

Hi Alex,

I understand you seek to interpret the result after using Discrete Wavelet Transform (DWT) function.

To clarify, Approximation Coefficients (cA) generally smooths out the signal, capturing the low-frequency trends. where as Detail coefficients (cD) capture high frequency details or transient components.

Given your signals behaviour It is likely that your signal has both low and high frequency components that are prominent. The similarity of both cA and cD to the original signal indicates that the signal's energy is well-distributed across different frequency bands.

To verify the integrity of the decomposition you can reconstruct the signal using the inverse DWT and see if the signal matches the initial signal.

reconstructed_signal = idwt(cA, cD, 'db4');
plot(reconstructed_signal);
title('Reconstructed Signal');

You could refer to the below MATLAB's documentation to know more about Signal Analysis in MATLAB.

https://www.mathworks.com/help/wavelet/signal-analysis.html