this post was submitted on 17 Aug 2026
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traaaaaaannnnnnnnnns
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If you have any questions, please ask. I love yapping.
yap
Let's say we have some periodic function f. The goal is to represent it as a bunch of sine waves. This is called a Fourier series (FS).
The FS coefficients are given by
⌠2⋅π
1 ⎮ -i⋅k⋅x
f̂(k) = ─── ⎮ f(x)⋅e dx
2⋅π ⌡0
for whole numbers k. We can then approximate the original function with
n
___
╲ -i⋅k⋅x
╱ f̂(k)⋅e
‾‾‾
k = -n
and make the approximation better by making n larger.
For non-periodic functions, we can still get an approximation! The Fourier Transform (FT) uses a continuous range of frequencies instead of whole numbers, and the sum is replaced by an integral (the inverse FT).
FT's are used everywhere, for example in signal processing and spectroscopy. If a recording contains an annoying high-pitched noise, we can apply the FT and filter the unwanted frequencies. Spectroscopy separates light into its different wavelengths. By comparing the resulting spectral lines with known measurements, we can determine which elements and molecules are present in stars and planets, for example.
idk what more to add ._.
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Today I have felt genuine happiness through the day after coming out to you all in c/chat. I caught myself smiling multiple times throughout the day when thinking about myself in a feminine way, using she/her pronouns and referring to myself by a new name in my thoughts. I haven't felt close to this way in a long time.
Last night I dreamed of getting my hair done, trying makeup and painting my nails. One of my dogs gets very loud out of nowhere during the middle of the night, so I woke up a few times, and every time I went back to sleep I got jumpscared by the image of a giant lesbian flag. I don't why because as far as I know I'm bi, lol.
Also I have decided to come out on BlueSky too, but maybe because I'm not a poster it got absolutely 0 engagement. Eh doesn't matter, the cool gay people are here anyway.
hell yeah
Hell yeag
so happy for you sister!
yay, thanks sis!