If you have any questions, please ask. I love yapping.
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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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Called my brother to come out to him, it went well. We don't talk very often and he's always busy, so I texted him to give me a call when he had a chance because I needed to tell him something. He thought it was going to be bad/sad news (it usually is when one or the other of us uses that phrasing) and was audibly worried when I finally talked to him. A few moments of stammering confusion that were a bit awkward (because I'm so awkward) later he understood what I was calling about and I managed to say what I needed him to know
Congrats
glad it went well. Coming out has always been difficult for me.
Thanks! Turns out me too, I knew it was going to be fine and I was still scared for no reason