cross-posted from: https://slrpnk.net/post/18727441
this post was submitted on 22 Feb 2025
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Wait, that's the graphical interpretation of the Fourier transform?
One possible way to show it. Makes sense to me
I’ve no idea what it is, so from my understanding it’s:
Changing the angle a wave is viewed from?
If that is the case, do waves have width?
I think the idea is that you can eventually get an approximation of whatever wave-like curve you want by merging several pure sin/cos functions with varying amplitudes, wavelengths, and offsets
Fun fact: this is mostly how JPEG works - it uses fourier transforms to approximate an image in a way that takes up much less storage than storing information about each pixel.
It's not supposed to represent waves at different angles.
Rather it represent an axis (the one on the right) for each frequency of waves that is contained in the signal (on the left)
Here the signal is made up of two different frequency waves and the graph on the right is there to show the value of thoses two and their respective magnitudes.
The axis going up is amplitude, the one going right and down is time, and the new axis rightward and upward (left to right on the right-hand chart) is frequency.
The left chart doesn't show the frequency axis. The right one doesn't show time.
The wave shown on the left in the dark cyan color is (shown to be) composed of two different waves of two frequencies shown on the left in gray and in the space between charts as dark cyan. The higher frequency one is lower amplitude.
It's a 90° angle for a reason.
Changing to some random angle may have sense for some theory, but it's not the Furrier transformation.
And no, the waves have 0 width. The widths on the drawing are for illustration purposes.