The Fourier Transform- Part II

A short tutorial video on how the Fourier Transform works. The video is designed for those who know what a Fourier Transform is but need to understand at a basic level how it converts time domain signals into the frequency domain.

Category:

Education

Tags:

• electrical
• engineering
• fourier
• transform
• time
• domain
• frequency
• signal
• analysis

[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.

[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).

[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.

[kordets]

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

[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 !!

[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