Parameters of Morlet wavelet (time-frequency trade-off)

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[pedrohenriquefloresmendes]

Amazing Mike, your videos are unbelievably good. I'm applying wavelets to detect the closing and opening time of a high-voltage circuit breaker for my thesis. Your understanding of the subject matter and clarity in explanations have helped me grasp mathematical concepts that were previously out of reach. I followed your entire course on signal processing on Udemy. You're a brilliant mind; keep up the excellent work. Wavelets are incredible; the uncertainty principle makes them unique.

[wwmheat]

perfect explanation, thank you!
P.S. couldn't help thinking about Heisenberg during the whole lesson..

[MrOuskit]

Very clear and informative, thank you!

[marchleslie]

Thank you so much! You are a great educator!

[varunmah]

Not sure how valid it is but the way I like to think about this is that wavelets with fewer cycles look more like impulses (i.e. delta functions) in the time domain, and therefore have a broadband spectral equivalent. As such, they offer less spectral resolution because they are capturing information across a wide range of frequencies. Wavelets with more cycles are closer to sine waves, and thus have a narrowband spectral equivalent (i.e their Fourier transform is closer to a delta function), and thus offer better spectral resolution. The effects of wavelet cycles in terms of time resolution are as explained in the video (i.e. smudging etc.)

[hadarhe]

Your vidoes are great! thank you so much for making this content

[bokkieyeung]

Hi Mike, I would like to ask about the "variable 3-10 cycles" option: do you mean we apply smaller number of cycles to lower frequency, and larger number of cycles to higher frequency? you mentioned the number of cycles is a function of frequency, i.e., dependent on frequency. why is that? I thought the "variable" to be "random" (apply a random number of cycle between 3 and 10 to each of the frequency). considering the relationship between number of cycles and time-frequency trade-off, is there any reason we give priority to temporal precision for lower frequency and to frequency precision for higher frequency?

[dongliu]

Thanks for your great explanation! I wonder how I can reference the figure at 15:17, thanks.

[fatemehmasoumi]

It was a really good lecture. thanks! I had a question. Dose any one know how to use morlet wavelet and stft Simultaneously in eeg signal preprocessing ? (I happened to read a "frontiers in neuroscience" article that used these two as EEG signal preprocessing)

[DL-vdmr]

Thanks. U video really helps. Is the cycle here the same as sub-octaves per octave in R？