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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  • gaystyleJoker [she/her]@hexbear.netMEnglish
    1·
    4 days ago

    HELLO THIS IS THE MEGA SIGN UP POST/LIST POST

    if you have a preferred week please tell me

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    ​ * after name denotes someone who has posted before and will be skipped by first-time posters

  • RondoRevolution [she/her, comrade/them]@hexbear.netEnglish
    8·
    16 hours ago

    I just watched the entirety of The Amazing Digital Circus in one sitting and wow. I cried so fucking much during episode 9. I didn’t think I would end up loving this show, but I just do. cat-trans

    spoiler for the show

    I now understand why there were so many trans Jax artwork 2 months ago, and holy fuck do I absolutely love her as a character! And precisely because she is so flawed. I cried so much when Isn’t She Lovely started playing. catgirl-cry

    It pisses me the hell off how all the comments keeps referring to her with the he pronoun on youtube. doggirl-growl

    I gotta admit, I thought I would end up hating her, because I thought she was just some mean bully in the first episode, but she just kept growing on me episode after episode.

  • scrungus [comrade/them]@hexbear.netEnglish
    17·
    20 hours ago

    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

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    9·
    22 hours ago

    I love black lacy clothing with goth vibes, but this shit is so expensive… The cheap polyester stuff is, well, not as cool and I don’t like it too much. Am I gonna have to learn how to make my own? Sounds too complicated