The Laplace Transform Table is the biggest crapshoot of a document I own because like I’ll hit a problem where I realize “man, gotta check the table to solve this” and sometimes it’ll be like
Okay fair.
And sometimes it’ll be like
And there’s nothing quite like the icy dawning horror of reading down the document realizing you haven’t found the proper structure of your expression until you’ve hit the 20+ region and by then it’s just too late there’s no saving your tragic soul rip in fucking pieces.
#YUP #laplace transforms are an exponential curve of increasing bullshit nonsense #basically this is a way to turn math from looking like something on one side of the column to the thing on the other side of the column #for no reason other than its how you solve the problem #its like you use a key to enter a door and once youre through you change what type of key you have with magic #in order to open a DIFFERENT door that leads you back outside again #but on the other side of the fence than you were at the beginning
This is the most genuine explanation of what the shit Laplace is Carlie I’m crying real tears
#theres some sort of law for some reason that proves all time-dependent functions can be modeled by a chain of specific sinusoids #(like infinite sinusoids) #and sinusoids can be fully defined w/o time just by amplitude phase and frequency so these smart asshats said ‘hey man’ lets invent a whole new system where we define our functions #as the integral summation of sinusoids #over the range of all FREQUENCIES #instead of time #so you basically juke your way OUT OF TIME YOU GIVE A BIG OL MIDDLE FINGER ‘FUCK YOU’ TO THE EXISTENCE OF TIME
These are my own tags BUT
I’ve been doing a shitton of studying into this concept of domain transformation for the last couple hours (ironically to avoid studying for my quiz shush)
I FUCKING GOT THIS. I JUST WROTE AN ENTIRE FUCKING PROGRAM FROM SCRATCH IN MATLAB TO PERFORM THE FOURIER TRANSFORM (and laplace is a type of Fourier). THIS WHOLE TIME-JUKING SIDE-STEPPING WIZARDRY WILD FUCKERY
For starters I fed it an input function built outta two sinusoids w/ frequencies 2 and 3 Hz respectively
BAM. DECONSTRUCTED. PERFECT PEAKS AT 2 AND 3 HZ.
1.5 AND 7?
WITNESS ME
2.7, 3.9, AND 6.78?
DEVOLVED THE FUCK OUTTA IT
IM LETTING THIS THING EAT THE GODDAMN GARBLED RADIO STATIC IN THE FIRST GRAPH OF EACH AND IT RIPS THE TIME-INDEPENDENT FUCK OUTTA IT FOR THAT BEAUTIFUL POLISHED WITCHCRAFT NONSENSE IN THE SECOND GRAPHS
WOW I SHOULD BE DOING HOMEWORK RIGHT NOW!!!
(my matlab function’s under the read more ifyacare)
This gif (which I made from this video) exactly summarizes the principle my code runs on to perform the transformation. Like the blue is the representation of the time domain data (down in the red bottom left) and the turning you see is the dude wrapping the function around a repeating circle at a varying rate, in this case frequency.
At non-matching frequencies the spread of the data creates a net zero vector, which is to say all the sin components and all the cosine components are degenerative and sum to zero and the resulting length of the vector you make is p much zero and that’s what the “frequency” chart on the bottom is drawing.
But when you roll through a frequency that resonates with some part of your time function (in his case the peaks occur at intervals of 2.2 Hz) the sin and cos components are NOT degenerative–they’re additive!! Cuz the peak occurs reliably at the same point in the circle at each pass cuz the data’s periodic frequency matches the rate of the circle’s rotation. And so you get a summed up vector with distinct non-zero magnitude that registers as a peak on the frequency graph.
So like, I watched the video and figured out this principle, and that bit of Matlab code under the cut is me translating this principle into mathematical instructions–like these three paragraphs entirely in Matlab instructions–so my computer would be able to perform the same kind of deconvolution
ANYWAY that probably made no sense but im still avoiding my real homework so i wanted to add this and now im probably done i almost promise
I SCREAM
So, running on like one hour of sleep, I just had an interview for a possible foreign exchange program with Denmark this coming fall. And (all these professors being engineers) they asked a kind of “what sets you apart?” and i answered p much “I’m a very self-motivated learner” and talked about how i built this monster last night cuz i fucking could
And they like…visibly found this neat. Like these are people with intimate knowledge of Fourier Transforms. And one of these professors suggested I try charting a Gaussian curve, cuz the transform actually gives back a different Gaussian curve but with differences in the standard deviation. A fat Gaussian input will yield a skinny Fourier output, and vise versa.
P much, if my code is working properly it should do this wide–>skinny, skinny–>wide relationship. So I just tried it
LOOKIT IT FUCKING WORKS MAN.
like…if it weren’t for the fact that they’re interviewing someone else rn I’d wanna like…barge back in and show em
IT WOOOOOOOOOOOOOORKS
okay but for real Chrissy, you’re a fucking inspiration
the fact that you can be passionate about damn near anything you get your hands on? I don’t know a single person who can do that. It’s like you honestly get a HIGH off of learning something new even if the subject is the bane of your existence – and that shit can’t be learned. That can’t be taught in school. That’s a fucking amazing trait that’s on the same level as a superpower.
The sort of passion that can make you do something tedious and ultimately useless “just because” usually only happens with one or two things for people; the one thing they’re best at, or their absolute favorite hobby. But you? You get to that level with anything that’s in your line of fire and I just. I’m ECSTATIC to see what good you do in the world.
Will you find a cure for cancer just because you surfed Wikipedia too long, ended up reading articles through the night, and spot something no one else has seen? Will you discover a way to suddenly make all renewable sources of energy immediately cost effective because you got carried away exploring a homework assignment way past the minimum requirements? Or the fountain of youth because someone just dared you to?
(okay a bit of an exaggeration maybe but honestly I ain’t ruling that shit out 100%)
I’m at the gym. They just played Evanescence’s “Wake Me Up Inside” followed immediately by Linkin Park’s “What I’ve Done”
Meme culture has ruined me because now I just want to burst out laughing. The emo stereotype is too strong. Self insert OCs are pouring from the windows. Lemon boyxboy don’t like don’t read. Ebony Darkness Dementia Ravenway is waiting impatiently behind me for the treadmill.
do people really think it’s called “wake me up inside”?
Attention Tumblr: It would appear the textpost I made on my iPhone while running was not thoroughly fact-checked. The song is “Bring me to Life” by Evanescence. We at phantomrose96 dot tumblr dot com do not endorse shoddy and inaccurate meme journalism, and so do dearly apologize for this error. We will make corrective efforts in the future to be better 2006 preteen goths.
Best vintage memes: O rly owl, numa numa, hampsterdance, caramelldansen, sparta remixes (the peak of this one was definitely “no, this is patrick), weegee, cdi zelda, over 9000, and, of course, longcat
backup 