How can I get a time-frequency representation of the resulted details and approximation signals from a discrete wavelet transform?

I am using discrete wavelet tranform to separate frequency bands from a given signals. My question is, How can I get a time-frequency representation of the resulted details and approximation signals from a discrete wavelet transform? there is any function to plot the frequency versus the time of such signals ? thanks

Answer 1

[Wayne King]

That is much easier to do with the continuous wavelet transform. You can certainly plot the wavelet coefficients with the appropriate spacing for the DWT, but keep in mind with the DWT the translation parameter is dependent on scale so that for level j, the details are spaced as 2^j*k, where k = 1,2,3,...

If you are really interested in visualizing a time-frequency analysis using wavelets, then the CWT is the way to go. You can construct the scale vector as you see fit.

[adam]

Thank you Wayne But my signal is a discrete one so I must show the frequency components and their localization in time for every detail signal, so I must use the DWT and not CWT. And in the case of CWT, how to visualize my frequency component in 2D plot ?

[adam]

Thanks a lot Wayne, I am waitin for your example.

Answer 2

[adam]

Thank you Wayne But my signal is a discrete one so I must show the frequency components and their localization in time for every detail signal, so I must use the DWT and not CWT. And in the case of CWT, how to visualize my frequency component in 2D plot ?

[Wayne King]

Hi Adam, you can still use continuous analysis for a discrete signal, the "continuous" here means that the translation and scale parameters are not restricted to be dyadic like they are with the DWT. I'll come up with an example today for both discrete and continuous and post it in this thread.

[adam]

Thanks a lot Wayne, I am waitin for your example.