Complex Morlet wavelet convolution

[@Avoide222]

Thanks a lot! I obtained a lot of intuition about using wavelets from this video

[@xic9631]

It is very clear and instructive. Thanks!

[@rabindranathdas8462]

Sir, It is very effective. I am new in this area. Would you be kind enough to show the path to get into the wavelet transform particularly into complex wavelet transform.

[@NicholasWong-vv1nn]

So is it reasonable to say that the un-needed information is essentially absorbed into the angle between the complex and real numbers, while retaining amplitude based on the project size?

[@marktodisco]

Around 11:30 you talk about repeating this process using wavelets with different frequencies (scales). Is there a limitation to the frequencies we are allowed to choose, or is the choice of frequencies (wavelet scales) arbitrary? Great video, and thank you in advance!

[@mikexcohen1]

It's a bit arbitrary in that you have more choice over the selection of wavelet frequencies compared to the Fourier transform. At the lower end, you're limited by the length of the time window (it doesn't make sense to have a wavelet at 1 Hz with a one-second segment of data), and at the upper end you're limited by Nyquist (you cannot extract frequencies above 1/2 the sampling rate). In practice, you would pick a range of frequencies that is reasonable for the characteristics of you data. For example, if you expect the important dynamics to be around 20 Hz, then you can pick wavelets ranging from 10 Hz to 40 Hz. I'm just making up these numbers, but it gives you a general idea.

[@wwmheat]

Thanks for the great explanation! You were saying that the narrowband filtered signal is the real part of the complex convolution. But does it mean that it is just a convolution with real cosine wavelet?

[@mikexcohen1]

Yes, correct.

[@murtazajallali]

i would love to see something about wavelet coherence analysis

[@mikexcohen1]

See playlist "ANTS #4"

[@princegarg5328]

Assuming the centers of real part of wavelet and complex part of wavelet are different. Will the product of real part of wavelet with signal and the product of complex part of wavelet with signal corresponds to the same time point while constructing the convolution time series?

[@mikexcohen1]

Interesting comment. The true center of the wavelet corresponds to the peak of the Gaussian. It *appears* like the center is lop-sided for the imaginary part, but that's because of the phase offset between real (cosine) and imaginary (sine). A complex Morlet wavelet is best thought of as 3D (time, real, imag), and in this space it has only one peak in terms of the instantaneous energy.

[@exec9292]

where is the code

[@ahsanayyaz42]

this is gold!

[@mikexcohen1]

Thank you, kind internet stranger.

[@murtazajallali]

this is gold

[@xyzant5069]

not enough compared with before videos

[@manfredbogner9799]

Sehr gut

[@mikexcohen1]

Danke :)