Wow... My professor took a month to explain this to our class and he DEFINITELY FAILED but this lecture is priceless. Fantastic. Thank you for your lovely lecture. No wonder Caltech is one of the best in the world
Wow, the "reciprocal space" look exactly like "x-ray diffraction pattern" in crystallography. They even have same function; the first encode images, the later encode crystal structures!
+xponen Nicely spotted, that's because it's exactly the same math! Nice to see how these complementary techniques eventually rely on the same mathematical basis
Thanks a lot for this video! I finally "get" the concept of FT in 2D, in crystallography this always still felt kinda like magic... But now it's clear. On to 3D!
The ⟨1,0⟩ wave at 10:50 looks like a sine wave, whereas the ⟨0,1⟩ at 11:20 looks like a cosine wave. I understand why cos(y) = cos(-y), but why since sin(-x) = -sin(x) why does the computer also generate duplicate amplitudes for the negative frequency of that wave too? And if it can't distinguish between ± frequencies, then why does the table of Fourier transform values have negative frequencies for one of the dimensions? Also what's the point of the phase for the ⟨0,0⟩ wave? Wouldn't all the necessary information just be in the amplitude for that wave?
As a convention, to keep things from getting redundant, h is kept positive. The negative h values would constitute the same wave functions as the negative k values already included.
I came across this video from a RUclips search for convolves. It seems to be part of a series, but I was unable to locate a playlist for it. Can someone post a link to the parent playlist, assuming such a thing exists?
Wow... My professor took a month to explain this to our class and he DEFINITELY FAILED but this lecture is priceless. Fantastic. Thank you for your lovely lecture. No wonder Caltech is one of the best in the world
Wow, the "reciprocal space" look exactly like "x-ray diffraction pattern" in crystallography. They even have same function; the first encode images, the later encode crystal structures!
+xponen Nicely spotted, that's because it's exactly the same math! Nice to see how these complementary techniques eventually rely on the same mathematical basis
clear! I love your pace of teaching. It is very comfortable! And I see you are really wanting to teach students something rather than show off.
You sir I just don't have a word but want to say thank you so much!
I like that duck
Thanks a lot for this video! I finally "get" the concept of FT in 2D, in crystallography this always still felt kinda like magic... But now it's clear. On to 3D!
28:53 It is the sort of things that will give me nightmares..
Joking aside, really really great series, I am learning a lot.
The ⟨1,0⟩ wave at 10:50 looks like a sine wave, whereas the ⟨0,1⟩ at 11:20 looks like a cosine wave. I understand why cos(y) = cos(-y), but why since sin(-x) = -sin(x) why does the computer also generate duplicate amplitudes for the negative frequency of that wave too?
And if it can't distinguish between ± frequencies, then why does the table of Fourier transform values have negative frequencies for one of the dimensions?
Also what's the point of the phase for the ⟨0,0⟩ wave? Wouldn't all the necessary information just be in the amplitude for that wave?
Wow, shifted me to a higher level. Thank you
9:48 I also struggle to say "Miller index" after saying "Miller indices" too many times XD
You are a great teacher! do you know that?
your pace is amazing
your voice is crystal clear
your approach is nice
Keep it up man
@@ibrahimelsayed5482 of course he knows that he's a renowned professor in one of the best institutes in the world
I think the h domain is actually -5 to 5 as k
As a convention, to keep things from getting redundant, h is kept positive. The negative h values would constitute the same wave functions as the negative k values already included.
@@TheMatt1doran But then, why isn't this done in the y-direction too?
I also dont understand
I came across this video from a RUclips search for convolves. It seems to be part of a series, but I was unable to locate a playlist for it. Can someone post a link to the parent playlist, assuming such a thing exists?
Yes, its actually about Cryo Electron Microscopy: ruclips.net/p/PL8_xPU5epJdctoHdQjpfHmd_z9WvGxK8-
3:25 I think y and x were mixed up here. Very nice lesson anyway!