The continuous Fourier Transform of rect and sinc functions (animation)

The continuous Fourier transform takes an input function f(x) in the time domain and turns it into a new function, ƒ̂(x) in the frequency domain.

In the first animation, the Fourier transform (as usually defined in signal processing) is applied to the rectangular function, returning the normalized sinc function.

[christinachu]

this video is 44s but I used 0.5x speed play and replay for minutes to understand XDD
it did give me a fresh and deeper understanding of FT!! Thank you so much.

[Raikaska]

Bear in mind that this happens because rect and sinc are even functions. When a function isn't even, it's transform's transform wont be itself.

[neeltej]

and thats the duality property of Fourier Transform 😎

[bcbrendan]

I just feel smarter anyway and I still have no idea what the hell just happened

[secondjar]

I have been thinking about it as if the time and frequency domain share the origin, it is interesting seeing this with the rect function delayed.

[josepaul]

What software did you use? I see the animation on wikipedia used the same format?

[_P_a_o_l_o_]

I‘ve got one question: what do the blue waves represent? I thought they were the oscillating factor e^(-2πixξ) - actually, their real part -, but when you do the Fourier transform of the sinc function these waves are zero for most of the time. Why? What do they represent? Thank you in advance

[ucasvb]

Custom drawing library on top of PHP+GD.

[fanatnauki]

Really great work!! Please tell me which program you made this video? Is it a 3DS MAX?