Thank you kindly, exoticcoder5365 :)

Glad it was helpful!

lol, making these videos is my night job ;)

In these times, even bad jokes can be useful!

lol thank you :)

Glad you like them! (The videos and the jokes.)

Thanks! Morlet wavelets are often used in time-frequency analysis, i.e., creating a spectrogram, which shows how spectral energy changes over time.

lol, yeah I think so. They're named after Jean Morlet, a French geophysicist. He was the son of Jean Mor, who invented the sine wave. (OK ok, that last sentence is just a joke.)

Hmm, that does seem to be the case. They're auto-generated. From some googling, this seems to happen sometimes with long videos, although this isn't my longest YT video. It doesn't seem possible to re-start the autogen process. I'll look into it, thanks for letting me know.

Great point, thanks Ranjit. Indeed, we always use complex-valued wavelets for the analyses, but I find it useful to start by introducing real-valued wavelets.

@@mikexcohen1 I must say, your videos are quite lucid and easy to comprehend and most importantly ..a good sense of humor.Good content and really love the color palette for the waveforms. Please keep up the good work.

Sure, you can apply wavelet convolution to any regularly sampled time series data.

Sure, you can use any tapering function. But a Gaussian is a great to use for several reasons, including the smoothness and spectral properties.

Glad it was helpful!

Yes, that's a good summary. Most "different" methods for time-frequency analysis are actually very similar to each other. Wavelet convolution has some advantages over the STFT (e.g., easier and faster to implement, fewer parameters), but the end result will be basically the same.

@@mikexcohen1 it seems like it would be slower to run, as youd need to run it for every frequency and time window: O(t x f) . Where was with STFT, you're only running for every time window (getting all the frequencies for that window at once): O(t)

@@mikexcohen1 I asked a question about this here: dsp.stackexchange.com/questions/68015/wavelets-vs-fourier-transforms

It depends on how you set it up and on how many time bins you have. Let's say you have 20 frequencies to extract. You need 1 FFT for the data, 20 FFTs for each wavelet, and 20 IFFTs. So that's 41 FFTs in total for the entire TF map. In neuroscience data analysis, we might have 2000 time points. If you extract 41 time bins for the STFFT, then the number of FFTs is the same, but 41 bins for 2000 time points is rather sparse. Furthermore, people often want to change the width of the time bins over different ranges of frequencies. Let's say you have three bins of frequency ranges with different time windows for the same center time point. So then the number of FFTs for the STFFT is actually 3N where N is the number of time time bins. To match the temporal resolution between STFFT and wavelet convolution, you'd need 2000 FFTs X 3 frequency bins = 6000 FFTs. So the way I've described it here, it's 41 FFTs for the wavelet analysis and 6000 for the STFFT analysis. But again, this is not trivially always the case; it all depends on how you set things up.

@@mikexcohen1 from what I've read, you've missed out the convolution step for the wavelet transforms. U use 41 ffts to the relevant frequencies, but you still have to do this for every time step - unless I'm confused.

YES thank you best wavelet intro on youtube!

Good question. One reason is theoretical: A Morlet wavelet is created by multiplying by a Gaussian [ exp(-x^2) ], and a Gaussian can never be zero; it can only asymptote to zero. The second reason is that due to underflow, digital computers have a hard time computing exact zero, so you end up with tiny numbers like 1e-16. On the other hand, there is a "practical zero" here where the values at the edges get so tiny that they have no real effect on the data.

@@mikexcohen1 Hi Mike, thanks for replying to that so quickly! It didn't occur to me that the Gaussian would also never be 0 but it makes sense from the way that it's calculated.

Yes, 2D Morlet wavelets are used for filtering images and feature-detection. Although image processing is increasingly done through deep learning models like CNNs.

@@mikexcohen1 Thank you very much for answer. I actually want to ask whether morlet wavelet can be used as kernel in convolution. Why is it not popular in image processing?

Yes, Morlet wavelets are commonly used as convolution kernels. They work great for signals and for images. A lot of image processing is moving towards ML/DL/AI techniques.

This whole series is in MATLAB. I have a bunch of other videos and courses in Python. I'm currently working on a course about deep learning in PyTorch, which will probably be finished in the summer...

@@mikexcohen1 thanks for the reply, I like your style

Nope, but the book that this course is based on has been translated into Python. See my github repo for the ANTS book for links. That said, I do have a signal-processing course (non-neuroscience-related) that is in both MATLAB and Python.

Aww... I love you too, aayushbajaj2260.