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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spoiler

  • gaystyleJoker [she/her]@hexbear.netMEnglish
    2·
    1 month ago

    HELLO THIS IS THE MEGA SIGN UP POST/LIST POST

    if you have a preferred week please tell me

    GayTuckerCarlson* (8/24 - 8/30)
Eco* (8/31 - 9/6)
Shaleesh* (9/7 - 9/13)
BountifulEggnog* (9/14 - 9/20)
sodium_nitride* (9/21-9/27)

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

  • lilypad [she/her, it/its]@hexbear.netEnglish
    28·
    1 month ago
    small win

    I went to the store. My sister got on the phone with me to help talk me through it. But. I went to the store. I bought food. I bought good food. Like, to cook. Not instant or frozen, but real, good, food. I didn’t have spoons to make it today. But. Tomorrow I will make myself a dinner worth eating. And it will be good. I’m proud of myself. The anxiety was strong. But. I did it. I went to the fucking store. Success. I hate that this is a big deal for me but this is the first time ive gone shopping shopping in a very long time. Even if its a little pathetic, I’m really proud. I’m debating going to the park again today. Ive been doing that as well, and have been proud of my ability to go out and be around people. But maybe not today. I’m tired. But proud. Prouds.

  • RondoRevolution [she/her, comrade/them]@hexbear.netEnglish
    28·
    1 month ago

    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. catgirl-happy

    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. rainbow-has

  • Sierra [she/her, they/them]@hexbear.netEnglish
    23·
    1 month ago

    Hey, my egg cracked and its been a sleepless couple of days. My mind has been racing about how I want to be, who do I come out to, imagining people’s reactions etc. Uh, what do I do now?

  • TerminalEncounter [she/her]@hexbear.netEnglish
    23·
    1 month ago

    Im in a different trans group chat with more local people, we do irl meet ups too, and the latest drama is someone left because I said there should be a moratorium on oversized pickups and you shouldn’t be allowed to drive anything larger than a 90s ranger size without a commercial license and for strict commercial purposes lol

    She loved her pickup more than a possible community (also I think she was shocked by how socialist and left wing trans people tend to be)

  • Sleepless One@lemmy.mlEnglish
    22·
    1 month ago

    A few days ago I experimented with using a new name with my therapist. I basically ugly cried the rest of the time. For some reason, I start panicking whenever I do something gender affirming. Hell, I feel like I’m gonna faint even when I try moving my pronouns from my bio to my display name.

  • SuperZutsuki [they/them, she/her]@hexbear.netEnglish
    19·
    1 month ago

    It’s getting to the point where I’m spending more nights in other peoples’ beds than my own and I’m fucking here for it except that everyone’s mattresses are too goddamn soft

  • Eco [she/her]@hexbear.netEnglish
    19·
    1 month ago

    doctors should devote all their energy to inventing a single pill that will make my brain normal. idc about anyone else i should be the priority tbh on account of my charming good looks and razor sharp wit