Continuous morlet wavelet

What is the different between complex morlet wavelet and continuous morlet wavelet?

Well, there’s a complex-valued Morlet wavelet and a real-valued Morlet wavelet. The former is made from a complex-valued sine wave whereas the latter is made only from a real-valued cosine wave. Complex wavelets are necessary for spectral decomposition, because they are robust to phase differences between the wavelet and the signal. Real-valued wavelets can be used for narrowband filtering.

Then we have discrete vs. continuous wavelets. They differ by being implemented on digital computers vs. being an analytic (symbolic) mathematical object. You can think about the difference between a sum and an integral, for example.

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Do you have a couple of references (elementary school level :slight_smile:) for Morlet wavelet spectral decomposition?

Well, I wrote a book about it. And have lots of videos on my youtube channel. And online courses on Udemy. So obviously I will recommend those references :wink:

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Dear Mike,

I watched two of your courses (Complete neural signal processing and analysis Zero to hero & Signal processing problems, solved in MATLAB and in Python), and thanks for these fantastic classes! These are really life-saving materials. But I still have a question. Can I anyhow make complex morlet wavelet or/and baseline normalization just for 1 channel and 1 trial (or all the channel but just for 1 trial)?

I need to make training set for Convolutional Neural Network from seizure EEGs and the morlet wavelet looks a reasonable choice.

Hi nyiba. Yes, you can definitely use wavelet convolution for one trial. Single-trial baseline normalization is a separate issue. I usually don’t recommend it, because the divisive baseline can be unstable. But your CNN will certainly need normalized data to avoid systematic biases. I wonder if z-normalizing is a better option here.

My recommendation is to make the normalization a hyper-parameter of the CNN pipeline, in that once you settle on a good architecture, try out a few different baseline/normalization options and see what gives the highest accuracy in the test set.

So in terms of the output discrete and continuous wavelet transforms are the same? I have a colleague asking how to do “continuous wavelet analysis”, is it just the same as using a complex morlet wavelet for time frequency decomposition?

Yes, they’re the same. But not all wavelets are complex Morlet wavelets. Otherwise, the mechanical principle is the same.

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Hi Mike, Could you please tell more about z-normalizing?
Thanks

I’m not sure what you mean. z-normalization means to subtract a mean and divide by standard deviation. It’s commonly used in statistics, machine learning, signal processing, etc. It’s just a way to get multiple variables into the same scale (mean of 0, stdev of 1).

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