Just wanted to chime in and say this man is clearly a fantastic lecturer! Very clear definition of what the goal of his teaching, explains every topic in ways simple enough you could probably show this to a high schooler and they'd be able to engage with it.
@@Eigensteve I'm glad you saw them :) I'm slightly jealous of your students - I'm currently Pershing my master's in Germany, and wish I had lecturers as clear as you in my undergrad & current post-grad program
Fourier was originally ridiculed when he first brought out this idea. Now it forms the basic of modern signal processing which covers pretty much every piece of thigh technology that we have. It goes to show why sticking to your convictions and going against the crowd.
Hi, Why (at 20:55) you supposed that there are exactly N-1 different frequencies? Maybe smaller number of frequencies is enough or, higher number of them is required.
Well, if smaller number of frequencies is needed then some coefficients will be zero. In discrete world, if you have only N points, you cannot get number of frequencies more than N (by the way, there are N frequencies not N-1, 0-s frequency also included). This is because discrete signals are periodic in time and in frequency. Just imagine that you have 5 points of data on a graph and all of their lengths equal to one, 0-s (0/N) frequency means that there are no oscillations (pulse train) , 1-st (1/N) frequency means that 1/Nth portion of an oscillation/cycle/period is done per one sample, 2-nd (2/N) frequency means that 2/Nth portion of a cycle is done per sample, ..., N-1-s (N-1/N) frequency means that (N-1)/N portion of cycle is done per sample, then if we go to N-s (N/N) frequency it means that entire cycle is done within a span of one sample, which means that nothing has changed it is the same as no oscillations at all. So there are only N distinct frequencies for N-point signal.
I've a few questions bothering me for a long time. These are as follows: Q.1 What if my graph of f verses x also has data points for negative values of x? How would I deal with that? Q.2 How did you decide the frequency axis while plotting the fast fourier transform? I didn't understand the meaning of the line: freq= 1/(dt*N)*(0:N); Please answer my questions.
Professor your appearance has not changed over the years, not even the hair! I never realized that learning hard topics like these can freeze the age of human 😁😆 I suppose that only brilliant genious like professor can achieve that, since the white hair on my head is growing exponentially over the years 🤣
Just wanted to chime in and say this man is clearly a fantastic lecturer! Very clear definition of what the goal of his teaching, explains every topic in ways simple enough you could probably show this to a high schooler and they'd be able to engage with it.
Thanks for your kind words :)
@@Eigensteve I'm glad you saw them :) I'm slightly jealous of your students - I'm currently Pershing my master's in Germany, and wish I had lecturers as clear as you in my undergrad & current post-grad program
Finally someone who builds it from the gound up and does the examples. thanks
Love your lectures! thank you from Russia!
You're doing so much for the world sharing this knowledge.
You are a Great Teacher. Thank you.
this video still good and actual, thank You!
Thanks!!! This saved my essay!
currently needing to learn DTF for my lab job on ion engine oscillation analysis, this is some good stuff
Nice
You building a Millennium Falcon or something ? :)
Well explained. Could understand well. Thank you. And that apple's idft joke. Lol
Fourier was originally ridiculed when he first brought out this idea. Now it forms the basic of modern signal processing which covers pretty much every piece of thigh technology that we have. It goes to show why sticking to your convictions and going against the crowd.
Exactly this. Not only he, but other scientists like Tesla were also laughed at.
Thank you.. that was helpful
I think n/N corresponds to x where is 2*pi*k it self shows omega(angular frequency) correct me if I am wrong
That is correct
Fourier Transforms are definitely more valuable in practice.
Hi, Why (at 20:55) you supposed that there are exactly N-1 different frequencies? Maybe smaller number of frequencies is enough or, higher number of them is required.
Well, if smaller number of frequencies is needed then some coefficients will be zero. In discrete world, if you have only N points, you cannot get number of frequencies more than N (by the way, there are N frequencies not N-1, 0-s frequency also included).
This is because discrete signals are periodic in time and in frequency.
Just imagine that you have 5 points of data on a graph and all of their lengths equal to one, 0-s (0/N) frequency means that there are no oscillations (pulse train) , 1-st (1/N) frequency means that 1/Nth portion of an oscillation/cycle/period is done per one sample, 2-nd (2/N) frequency means that 2/Nth portion of a cycle is done per sample, ..., N-1-s (N-1/N) frequency means that (N-1)/N portion of cycle is done per sample, then if we go to N-s (N/N) frequency it means that entire cycle is done within a span of one sample, which means that nothing has changed it is the same as no oscillations at all. So there are only N distinct frequencies for N-point signal.
@@torebektoregozhin4626 Thank you so much.
I SEE IT. Thanks.
I've a few questions bothering me for a long time. These are as follows:
Q.1 What if my graph of f verses x also has data points for negative values of x? How would I deal with that?
Q.2 How did you decide the frequency axis while plotting the fast fourier transform? I didn't understand the meaning of the line: freq= 1/(dt*N)*(0:N);
Please answer my questions.
when you have \omega_n = e^{-2pi/N } Is this you converting the matrix back into the natural basis. as opposed to the cos + i sin basis ?
8:00 Why the first order polynomial be a zero slope line?
Professor your appearance has not changed over the years, not even the hair! I never realized that learning hard topics like these can freeze the age of human 😁😆 I suppose that only brilliant genious like professor can achieve that, since the white hair on my head is growing exponentially over the years 🤣
sir i want lecture on discrete fractional fourier transform (DFRFT)
He looks like an American version of Lee Joon-gi