Introduction to the Fourier Transform (Edited)

This video is made available under the Creative Commons BY-SA license.

[DarrylMorrell]

The easiest way to do a Fourier transform of a triangular pulse is to use the fact that the triangular pulse is the convolution of two rectangular pulses, and that convolution in the time domain is equivalent to multiplication in the frequency domain. So the triangular pulse transforms to a sinc squared function. I don't have a video illustrating this for continuous time signals; I do have one for discrete-time signals, which you can find by looking at my "Discrete-time Signals" playlist.

[DarrylMorrell]

If you know the inverse transform f(t) of a particular *bilateral* Laplace transform F(s), and the region of convergence of the Laplace transform includes the imaginary axis, and you have a Fourier transform which is F(jw) [where s has been replaced by jw], then the inverse Fourier transform of F(jw) is f(t).

[NicolasJosephScozzaro]

I like the phone ringing in the background at 7:05 Ha!

[TheProudMisogynist]

do you know how to do a fourier transform from triangular pulse? thank u
(sorry for my bad english)

[Frey]

at 7:22 why is it that when you replace s with j*(omega) that you get X(omega) = ... and not X(j*( omega ) ) = ...?

[GizmoMaltese]

Because the function on the right side is just a function of omega. That's all that notation means.

[Leon-pnrb]

your voice sounds like as if you are depressed af and yet you are forcing yourself to make this video
it was so powerful that it made me depressed and sleepy

[abdibasetalinor]

yes you are right but for simplicity he wrote X(omega)...but it's originally X(jomega) ..don't get missed :)

[Frey]

Oh, right! because omega is the only variable, j is just a constant!

[bernarddoherty]

Get something to drink please and Clear your throat please!!! Nice video but do it over. I had to stop listening. Drove me nuts listening to you. Maybe has something to do with myself being a singer. Just couldn't tolerate it.