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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Why do we feel like shit
Oooooh
I need a good breakfast that requires zero cooking so I stop needing to hold in bitchiness at work in the mornings.
Sometimes I make a sandwich and stick it in the refrigerator overnight
Ahh yes, but you see, this requires me to brave the grocery store, something only possible on a new moon when the humidity is high and the temperature low with no clouds and enough tree leaves on the ground (I'm overwhelmed by grocery stores and have no pb or j or bread in the house. I will go shopping someday.... Someday.... I already went recently... I can't go again so soon)
Some things will forever remain a mystery. No one will ever know.
Yeah... I started eating more than one meal a day recently and I've been feeling better mentally. So I got that going for me for a couple weeks til my mind decides arbitrarily its gross to eat food again