The Fourier Transform- Part II

[ap41591]

Instead of doing just one integral, we can just do two!

[TranceTips]

lol. prepare for pain. My brain goes: "YAY! I'm gonna be a masochist today!"

[JustAnAdjunct]

"...you've experienced pain whenever you've seen integral signs..." quoted for truth

[MRTWW555]

Thanks for uploading!!



[Anushsudha]

thanks. this is better than reading from books. though i have problems with the integrals. preparing for my post graduation and need to recall them

[Doonskaia]

excellent tutoring way !!

[lrgopal2009]

Excellent! Very short and good lecture. Can you provide the similar lecture on the following topics.

Fourier Series.

Laplace Transform

Difference between Fourier and Laplace Transforms.

[kridnix]

@lrgopal2009 I am working on a series on electromagnetics now, but I am taking a break from being a faculty member and so it is slow going.

[Suyamu]

thanks for the video.

I study computer science - and our professor in signal processing class usually doesn't care much about explaining stuff - thinking in algorithms is much easier for me to understand than mathematic theory behind it.

[tatfr0guy]

not to be an idiot at the wrong time but 1:00 - 1:04 thats what she said

[nemo21us]

Did anyone get this part: ".... by solving this differential equation at one frequency, omega, and turning it into an algebra equation I know the solution for all frequencies ..."?

[kridnix]

@nemo21us Given a differential equation a*d^2f(t)/dt^2 + b*df(t)/dt + c*f(t) = 0. If I solve for the case f(t) = exp(j*w*t) then d^2f(t)/dt^2 = -w^2*exp(j*w*t) and df(t)/dt = j*w*exp(j*w*t). If I plug these in to the differential equation I can divide both sides by exp(j*w*t) to get -w^2*a + j*w*b + c = 0. Voila, algebra. Since I can make any f(t) from a sum of exp(j*w*t) due to the Fourier transform I solved my differential equation for *all* possible signals, f(t).

[thavamaran]

You are exactly describing the thing that is happening to me!! What I meant was about the brain shutting down, but eventually im overcoming it now....cheers! Fantastic lecturing style, love it...

[jimmyshitbags]

"gah, prepare for pain!!!!!" hahaha

[kridnix]

You just have to believe deep down that there can be completely different ways of looking at the world that are equivalent. Our human bodies see the world as a series of moments in time. The physical world seems to act as a bunch of sinusoidal waves of different frequencies all happening at the same time. Fourier showed that both these views are equivalent.

[kridnix]

Unfortunately I am a physical optics guy. If I can find the time I might take a stab at those.

[rcaccese]

@kridnix Very nice explanation. I'm a radiologist with a specialty in MRI. I've always thought of Fourier transform as a black box that processed the signals emitted from the relaxation of protons in a magnetic field after being excited by a radio frequency. I still don't understand it (after 20 years of study) but I feel I'm getting closer. Thanks.

[system0system0]

why dont you do a explanation of jitter, ISI, BER etc...

[kridnix]

Thanks. I did these videos on a whim and I'm glad so many people find them useful.

[nashixe]

This is one of the most clear explanations of Fourier analysis I've seen, on Youtube or in lectures.

[wenaolong]

Thanks for saying "forward" correctly. Forward is derived from "Fore" and "Ward" not from "Foe" and "Ward". Thanks.

[snorbaard777]

"So let's understand, now that we've got the basics out of the way, how the Fourier transform REALLY works: Let's go in and see the mechanics of the bloody thing." This made my day :D

[system0system0]

Thank you Claude Shannon for making possible the information age

[kordets]

I fell on the floor when he said 'Now, instead of one integral WE CAN DO TWO INTEGRALS' :DDD

[yyback]

dead~ prepare for pain~

lol

[ApteronotusL]

Hi Kridnix, Excellent video! Thank you.

I have one quick question. If you change your function f(t) into a sum of sinusoids as you explain (2:19) and plug them into the diff. eqn you get a sum of the form:

SUM{ F(w)exp(jwt)*(-w^2-ajw+B) }=0

I dont see how this can be solved algebraically as was the case when we only had f(t)=F(w)exp(jwt).

So my question is how does this assist us in solving the diff eqn for an arbitrary function?

Thank in advance.

[wrodusa2006]

Hi Kridnix, Its a nice explanation..I have a a question for you...do you know some software free for integrals and science and engineering applications?

Thank you..PJ

[kridnix]

Not off the top of my head.  I am a long time Matlab user so never had thet need to use any free software.

[Pudersepp]

There probably is no good free software for such applications. Your best shot is get a ripped version of the program, or ask your local uni. for a program with their license.

[zoso95]

@wrodusa2006 wolfram alpha

[zoso95]

@wrodusa2006 wolfram alpha

[dramljak1]

@wrodusa2006

Scilab is a great alternative for MATLAB, it has almost the same power.

I used it parallel to MATLAB in my DSP classes and it only doesn't work with IIR BP filters because it doesn't retrive enough numbers after decimal character.

[leocmen]

@wrodusa2006 Try GNU Octave, for sure that is not a Mathlab, but it is very fair for some activities.

[pefirme]

Thanks

[taurus040588]

Spot on, as soon as i see differential or integral and weird signs i give up haha

[ee04395]

thank you

[rabinEXPRESSO]

i don understand the second reason(differential equations and its significance) at 3.00.

[kridnix]

I had to assume you know what differential equations are and also the properties of exponentials. So IMHO differential equations are a bitch to solve, you basically look up the solution. The Fourier transform allows you to solve differential equations using algebra relatively easily as long you have a solution of exp(iwt). This type of solution is a wave and frickin practically everything can be written as a sum of waves. Basically you have to accept the importance and prevalence of waves.

[vinvonvin]

Thank you. At last I got an intuitive explanation that I had been searching for !!

[camel04]

Thanks, I am a practicing engineer and this was a great refresher.

[pharloo]

thanks for uploading this useful lecture.