3 ms·
> This means that the signal and spectrum are both sampled discretely and not continuous as that would not be possible on a computer. I mean, true in a technic
by MauranKilom 5y ago
> This means that the signal and spectrum are both sampled discretely and not continuous as that would not be possible on a computer.
I mean, true in a technical sense, but don't all the sample functions here have known analytical Fourier transforms?
One of the coolest parts about this (in my eyes) is seeing how a time shift causes a linear phase rotation in the frequency domain. But one has to choose the parameters very carefully to avoid stark aliasing (not in the Nyquist but just the "see individual line segments" sense). I would've at least hoped for a "sample count" or similar slider to control the sampling resolution.
It would also be cool to have functions in the shape dropdown that are not symmetrical. For example, I read the side text about "Taking the Fourier Transform twice results in the original signal flipped along the time axis." and wanted to try that - but with symmetrical functions the flipping is not evident. Sure, introducing a time shift did the trick, but it was a tiny disappointment.
Btw, contrary to other comments here, I like the cube visualizations and I think it makes some sense. I mean, it doesn't significantly advance my understanding/intuition by leveraging some geometric relation between the cube faces [1], but just having 3D plots of both time and frequency domain is novel to me.
[1] Although I will admit that this will help me in picturing the "apply four times to get back the original function" (does this have a name? Double-involution?).
- laszlokorte 5y ago> I mean, true in a technical sense, but don't all the sample functions here have known analytical Fourier transforms? Yes but currently I make not use of it but simply apply the DFT on the samples of the function. Making use of the analytical versions would result in smoother results but I would like to allow for custom signal functions in the future so I would like to keep the simple approach of just doing the DFT. > It would also be cool to have functions in the shape dropdown that are not symmetrical. Nice idea but what interesting functins would be there that are not achieved by using the time shift? > Sure, introducing a time shift did the trick, but it was a tiny disappointment. I agree
- MauranKilom 5y ago> Nice idea but what interesting functins would be there that are not achieved by using the time shift? Well, a sawtooth for example? PS: You need two line breaks to have your replies in a separate line.
- laszlokorte 5y agoAh yeah, thanks, I added a saw function.