Lecture 3 | The Fourier Transforms and its Applications

[sarojunique]

excellent sense of mathematics with science which rarely exists

[TheBassamassad]

Great Lectures!

[ankur29]

@ gachmari go to the link in the description

EE 261 at Stanford University

eeclass.stanford.edu/ee261/

[chimpspecialist]

2 much writing.

[gachmari]

where can i get notes ???

[Spasatcom]

cool and nice video, Button depressed like ^^___^^

[grunder20]

I havent seen such amazing lecture.

[seniorbooboojuice1]

Does anybody have any thoughts on Tolstov's Fourier Series? I'm thinking of reading that along with this.

[orion2020]

lol at 13:20 hahah this lecturer is awesome!!!!!

[jbxf]

Personally, I'm a fan of those epsilons and whatnots. I'm not fully comfortable with the way he omits that question about pointwise convergence.

[MeganJ29]

long-winded, but very intuitive

[nimbusiness]

I didn't know Kermit the Frog taught calculus at Stanford.

[originalparis]

13.30 Nobel Prize!

[ITGProphet]

That middle blackboard is annoying me, and I'm not even in the room.

[iBradleyAllen]

at 32 sec, Smoother the function, the faster it converges? how is 'degree of smoothness" defined? what does Uniform Convergence mean? How close the approximation of the original signal to the discrete sampled function, if closer its smoother?

[gomunkul]

@iBradleyAllen i think he will talk about it later. if not, that info is readily found on the net (the good thing is that you have very exact questions).

[MrFattyBongo]

that middle blackboard isn't convergent haha

[TooMuchGass]

Most students who are integrating functions, dont even know what they are doing.

Much less what they are doing when they are transforming functions

[cpinnago]

Thank you so much for this.....this greatly helped me to understand concepts in my "medical imaging - Signals and systems" class. Thank you kindly.... :)

[foboi1122]

haha omg i love this guy!

[chaidaro]

LOL at french

[gomunkul]

@chaidaro outrageous !

[dankheads]

These lectures are amazing

[ngocmath]

Great lecture! Thanks so much for uploading. Hope Stanford uploads more and more lectures like this.

[alquiora]

I have a question. I agree that the sum of the Euler's formula from -n to n is a real number but since that it is the sum of the conjugates that also means that the only term left out of the sum is the cos function which is the real part. So doesn't that indicate that the the sum of Euler's formula is not equal to the sum of cos + sin?

[sikory]

that is the case when all the c_n's are real, in general they are complex numbers and in that case the sin factors don't cancel just try it with an example: c_-1=1+i and c_1=1-i

[kevinatucla]

who cares? My question is: how can we apply this in real world? While everyone of us uses LCD TVs and laptops and cellphone...only very few...very very few of us know how these things are built and how just 1 Japanese company (Casio) can have a factory that can produce 100,000 digital cameras/month in an UNMANED (there is no human in the factory) factory?? I like these lectures but again how much is Standford really showing us of the truth?? And how can they help more people know the truth?

[alquiora]

@kevinatucla

Haha... I hope that you're not in college yet. Pity....

[kevinatucla]

alquiora, your respond is vague. I have already graduated from UCLA but unfortunatly in a non science major. Again,let me emphesize that I love these lectures and what Standford is doing. My point is I guess that many many students (mostly asians,Indians,or even white students) they just learn things to get a good grade and move on.They don't think in terms of WHY they are learning it and when exactly they would use it.I wish the teacher started the series by saying this has to do with diffusion

[alquiora]

@kevinatucla

It's very clear that you do not see what Math is. I advice you to read more to stop being... well I said it earlier.

[kevinatucla]

I do that when you learn more English.

[alquiora]

@kevinatucla

A graduate of UCLA? What a joke!

[chaidaro]

@kevinatucla - Dude... People like me took this course because I wanted to appreciate the beauty of mathematic and to answer all of my curiosity. You have a problem with that?

[arnshea]

Prof Osgood is amazing. His enthusiasm is infectious. Hearing (and seeing) his mathematical insight is a privilege.

[jalalmalo]

can u allways interchange the sumation and the integration? If not could someone please give an example, thanx

[DanMan7997]

Yes, you can always interchange the summation and integration. For more info on this check out the Wikipedia article "Sum rule in integration".

[jc7vergara7]

No you can't. a sum becomes integration only when you take the limit of an infinite sum and the change in the variable approaches zero. That's why he talks about error estimation.

[bflast]

Remember that summation and integration both are linear operations

[marcpiggott]

Provided you have uniform convergence...

[ArtinEmil]

Uniform convergence only comes up when you are dealing with infinite series and you want to integrate term-by-term. The professor was integrating a finite (regular) sum and so one does not need to be concerned about uniform convergence.

[Mattprole]

I've read that you can, and that there is an intricate proof of this. I am not aware of the details though.

[ArtinEmil]

The proof is actually easy. If f_n is a sequence of integrable functions on [a,b] and f is the limit function, also integrable on [a,b]. Then |f_n - f| < e for n sufficiently large. So,

| int_a^b f_n - f | <= int_a^b |f_n - f| <= (b-a)*e

Since (b-a)*e can be made arbitrary small we have convergence.

By the way, you can drop "if f is also integrable on [a,b]", part because uniform convergence preserves integrability, but that is a bit harder to show.

[anunez20]

hello, somebody knows where ca i get the "sinesum2" Matlab program?

[djkeogan]

The course materials can be downloaded from the "Stanford Engineering Everywhere" site. (Can't seem to post URL here... Google it).

[rammps1982]

great!

[NotJames1]

this guys handwritting is so bad

[xinliw]

thanks for sharing~

Prof. Osgood is so good lecturer

[xinliw]

I'm from math and this course really helps me a lot. Can you make audios of courses from math division as well?

That would be really great!

[akiforu]

Thanks

[Emiel84]

Did watch this one to :) . Want to thank you all for this amazing video !