Time Frequency & Multi Resolution Analysis

[@megahady]

Fantastic explanation as usual. Thanks, Nathan!!

[@ashkan00021]

Absolutely amasing , the best ever course on wavelet ever watched in your series of wavelets!

[@apferrero07111962]

Great my compliment

[@ginebro1930]

"Maybe you can have trust in yourself... or maybe not" hahahaha that line cracked me Nathan

[@JimD20619]

If you could, please create a time machine and teach with the Physics department at Rutgers during the late 80s. ... ... Oh, well, obviously that didn't happen. Thought I'd give it a shot.

[@williamlivernois7286]

3:04 should be delta(m,k)delta(n,l). I know that's really minor but I got stuck on that for too long :P

[@somyasharma7332]

WOW!

[@samidelhi6150]

Hi professor. Great exposition , is it because of property ( IV ) that if you're handed an aggregate datasets ( let say daily electricity prices ) you can't recover the tick components of such aggregate dataset ! But on the other hand if you're handed the original components i.e ( tick resolution) then you can with ease recover the daily aggregate price dataset via a function say like " resample" in Python or any equivalent ? Kindly confirm if this the case , Secondly would you direct me to any sources like written programs in Matlab / Python where I. can see an example ( MRA) merged within ML framework like Q-learning ?am thinking of how using MRA-generted features to render a more powerful algos within RL environment Your input is highly appreciated

[@aoliveira_]

It's the Kroneker delta, not Dirac delta.

[@Thecommet]

These are great lectures, I'm having fun learning and you explain everything in an intuitive way! I do have a few questions though that I don't understand. 1) You showed how the variance/power of the signal is calculated, both in regards to the CWT and the Gabor transform, and in both of these cases I don't see the signal function (let's call it f(t)) in any of these formulas. It's just sigma^2 = int_{-inf}^{inf} (tau-t)^2 |g(tau)|^2 dtau. The way you presented it, this should somehow involve the signal f(t) but the formula seems to calculate the variance of Gabor's "new Fourier Kernel" (or in the case of wavelets, calculate the variance of the wavelet itself). What's even stranger to me is that if I try to calculate the variance using e.g. the Haar wavelet, I get sigma^2 = int_{0}^{1} (t-tau)^2 dt = 1/3-tau+tau^2. This seems to suggest that the further away I get from the wavelet's center, the higher the variance becomes? This seems really wrong to me. 2) This is also in regards to the variance: In your formula you square the wavelet function and the gabor kernel. Why? The variance function I learned is sigma^2 = int_{-inf}^{inf} (t-tau)^2 f(t) dt 3) Gabor transform: I'm finding a lot of discrepencies between what you wrote and what's on wikipedia. A factor of 1/2pi is missing in the inverse transform and g(t)=e^(-pi*t^2) instead of g(t)=e^(-t^2). Sure, in the end the concepts are the same but I'd like to understand what exactly these factors influence. Thank you for your time and I hope you continue making lectures!

[@daniela16xx]

6:21 it should be L/2 instead of 1/L