Anonymous at Sat, 1 Jun 2024 09:12:01 UTC No. 16203854

>>16203852
It allows you to transform integration and differentiation in the time domain into much simpler multiplication and division.

Anonymous at Sat, 1 Jun 2024 09:13:33 UTC No. 16203857

>>16203854
You just googled that shit you cocksucker

Anonymous at Sat, 1 Jun 2024 09:14:37 UTC No. 16203858

>>16203857
Just because you couldn't

Anonymous at Sat, 1 Jun 2024 09:16:15 UTC No. 16203862

>>16203852
>Laplace transform
oh I hated that shit. lol

Anonymous at Sat, 1 Jun 2024 09:36:58 UTC No. 16203893

just another trick for solving diffy Qs what's the problem?

Anonymous at Sat, 1 Jun 2024 10:52:30 UTC No. 16203959

it just shows how much a decaying cosine the signal is. git gud.

Anonymous at Sat, 1 Jun 2024 11:34:29 UTC No. 16203989

>>16203852
I prefer f(st)*e^(-t).
It transforms the exponential generating function of a sequence into the ordinary generating function of the sequence.

Anonymous at Sat, 1 Jun 2024 11:41:24 UTC No. 16203998

>>16203852
You learn this in the very first lecture of any decent signals and systems course. May God have mercy on your midwit soul if you get filtered by this.

Anonymous at Sat, 1 Jun 2024 11:42:09 UTC No. 16204000

>>16203852
its literally just for academic pseudointellectual mental masturbation and comparing metaphorical dick sizes of the mathematical part of the brain

Anonymous at Sat, 1 Jun 2024 11:44:10 UTC No. 16204005

https://youtu.be/n2y7n6jw5d0

Anonymous at Sat, 1 Jun 2024 12:39:07 UTC No. 16204064

>>16203852
Any function can be written as a linear combination of any other orthogonal basis vectors. It's like tilting your head at a girl to see up her skirt. The panties are there but a different perspective helped you see it. Sometimes you need a fourier perspective. Sometimes you need the Laplace perspective. That's all there is to it. Do you want to see the panties anon? Now, sure you can look at that hot piece of ass all you want while she has her tight cocktail dress on. But unless you get the right angle you're not going to see those panties.

Anonymous at Sat, 1 Jun 2024 12:40:49 UTC No. 16204065

>>16203852
The Laplace transform is goated. It is probably the most useful linear transformation out there.

Anonymous at Sat, 1 Jun 2024 12:48:11 UTC No. 16204071

>>16203852
Representing a function as an infinitesimal sum of damping or amplifying oscillations. Much stronger that fourier's shit

Anonymous at Sat, 1 Jun 2024 13:13:57 UTC No. 16204113

For me, its the Fourier Transform

Anonymous at Sat, 1 Jun 2024 13:15:12 UTC No. 16204118

>>16203852
It's just a better behaved Fourier transform

Anonymous at Sat, 1 Jun 2024 13:19:22 UTC No. 16204127

>>16204064
This. It's no different than identifying eigenvectors or working out canonical transforms or switching to some kind of center of momentum frame or comoving frame or non-inertial frame or any of the other million similar techniques:

90% of solving mathematical and physics problems is figuring out the right 'angle' to look at the problem that makes the solution obvious.

Anonymous at Sat, 1 Jun 2024 16:42:10 UTC No. 16204701

>>16203852
For a Fourier transform you can see how it's composed by frequency. For Laplace, you get a combo of frequency and exponential decay functions

Anonymous at Sat, 1 Jun 2024 17:07:35 UTC No. 16204796

>>16203852
> as contrived as possible for no fucking reason whatsoever
Ok dude have fun in the time domain trying to figure out if the thing you build will explode when subjected to oscillations.

Meanwhile I’ll just take the laplace transform, find the roots of a simple polynomial & be done in 2 minutes

Resolve !!EVGgx2S/Lta at Sat, 1 Jun 2024 17:31:14 UTC No. 16204863

>>16203852
It allows you to turn a differential equation into an algebraic one. It's an immensely useful tool.

Anonymous at Sat, 1 Jun 2024 22:31:51 UTC No. 16205260

>>16203852
Watch this playlist:
https://m.youtube.com/playlist?list=PLldiDnQu2phvCb1QQhanJYm7A6xzEoC3F

Anonymous at Sat, 1 Jun 2024 22:41:58 UTC No. 16205281

Idk bro I do ecology, hehe!

Anonymous at Sun, 2 Jun 2024 02:23:27 UTC No. 16205595

>>16203852
disregard everything said so far in this thread. a quick glance at wiki says how the laplace transform came to be. in fact euler and laplace came upon such methods in their studies of probabilities, it had nothing to do with muh time domain and muh fourier. engineers wrote that
https://en.m.wikipedia.org/wiki/Moment-generating_function

tldr; if you study probability you will encounter such methods in a more natural setting

Anonymous at Sun, 2 Jun 2024 03:42:27 UTC No. 16205709

>>16204000
>t. non engineer

Anonymous at Sun, 2 Jun 2024 03:44:56 UTC No. 16205713

>>16203852
>What the actual FUCK is the purpose of this fucking SHIT?
Solve linear differential equations quickly and easily.

Anonymous at Sun, 2 Jun 2024 03:45:57 UTC No. 16205715

>>16205595
>engineers wrote that
THOSE EVIL LYING BASTARDS!

Anonymous at Sun, 2 Jun 2024 03:56:47 UTC No. 16205730

gives solutions to differential equations

Anonymous at Sun, 2 Jun 2024 07:08:22 UTC No. 16205859

>>16203852
F(t). S.t . T.dt. = -1


????

Anonymous at Sun, 2 Jun 2024 08:27:20 UTC No. 16205926

>>16205595
disregard everything said so far in this thread. a quick glance at wiki says how the fast Fourier transform came to be. in fact gauss came upon such methods in their studies of interpolating the motion of planets, it had nothing to do with muh signal processing and muh solving PDEs. engineers wrote that
https://babel.hathitrust.org/cgi/pt?id=uc1.c2857678;view=1up;seq=279

tldr; if you study orbital mechanics you will encounter such methods in a more natural setting

Anonymous at Sun, 2 Jun 2024 08:28:21 UTC No. 16205927

>>16203852
You know how you show your disdain for all these French bastards? You mispronounce their names. Not pronouncing a man's name properly is the ultimate slight. I give you LAP-LACE.

Anonymous at Sun, 2 Jun 2024 13:46:50 UTC No. 16206132

>>16203852
making stuff easier for us retard engineers. thank you for your service, nerds.

Anonymous at Sun, 2 Jun 2024 14:12:45 UTC No. 16206171

>>16203852
>What the actual FUCK is the purpose of this fucking SHIT?
Control theory.

Anonymous at Sun, 2 Jun 2024 20:47:35 UTC No. 16206686

>>16205926
>laughs in methmatics

Anonymous at Sun, 2 Jun 2024 21:00:30 UTC No. 16206719

>>16203862
Personally, after spending hours on variation of parameters problems and various other cancerous methods in ODE I was overjoyed when I saw the power of Laplace transforms.

Anonymous at Sun, 2 Jun 2024 22:19:04 UTC No. 16206857

>>16206719
You can just learn how to factor differential operators.
Then you can just solve things directly.

Anonymous at Sun, 2 Jun 2024 23:58:10 UTC No. 16206996

It's like log in that it converts a difficult problem into a simple one

Anonymous at Mon, 3 Jun 2024 03:35:30 UTC No. 16207209

>>16205927
>LAP-LACE
Can someone vocaroo this? Not sure how this is supposed to be pronounced

Anonymous at Mon, 3 Jun 2024 04:13:33 UTC No. 16207243

>>16207209
/ˈlæpleJs/

Anonymous at Mon, 3 Jun 2024 13:43:29 UTC No. 16207811

>>16207209
La-plah-Ssss

Anonymous at Mon, 3 Jun 2024 22:22:27 UTC No. 16208510

No one has answered my question yet what the fuck

Anonymous at Mon, 3 Jun 2024 22:41:50 UTC No. 16208562

>>16208510
It changes coordinates from time to frequency, there are you happy?
Why this is useful is that it allows you to perform algebra with the boundary conditions of the given DE
[math]\mathcal{L}\{f'(t)\} = sF(s) -f(0)[/math]

Anonymous at Tue, 4 Jun 2024 09:39:30 UTC No. 16209478

>>16203852
If you want the real answer, it is that it allows you to solve differential equations involving terms that are not technically functions, called tempered distributions. The most famous example is the delta distribution, and it pops up in control theory, where a short, but very intense, signal can be represented as such. It also satisfies nice identities with the convolution operation, which makes it a handy tool.
See: >>16205260

Anonymous at Tue, 4 Jun 2024 09:44:34 UTC No. 16209484

>>16203852
it's very useful, you can solve differential equations with it really quickly.

Anonymous at Tue, 4 Jun 2024 09:46:14 UTC No. 16209486

>>16204118
isn't the Fourier transform a generalization of the Laplace transform?

Anonymous at Tue, 4 Jun 2024 09:54:03 UTC No. 16209491

>>16204000
you'll understand when you finish high school and start your engineering degree.

Anonymous at Tue, 4 Jun 2024 10:29:51 UTC No. 16209521

>>16209486
The two sided Laplace transform is the same as the Fourier transform with [math] s = i\omega [/math]
The one sided Laplace transform is actually substantially different, because restricting the domain means that the initial conditions enter explicitly, and the integral can converge for exponentially decaying or growing solutions where the Fourier transform does not.
In certain situations where there is exponential behavior that depends on the initial conditons, the Fourier problem of finding normal modes of the system can be ill posed, and will gove incorrect solutions when naively applying Fourier analysis, which means it must be treated as an initial value problem and solved via Laplace transforms. See the attachment for a physical example of where this difference matters.

Anonymous at Tue, 4 Jun 2024 11:04:17 UTC No. 16209549

>>16203998
>You learn this in the very first lecture of any decent signals and systems course
you learn to follow the recipe
I do not think you learn what it actually means

Anonymous at Tue, 4 Jun 2024 11:17:07 UTC No. 16209571

>>16209549
isn't it incredible how shitty the education system is?
they teach you what the screwdriver is and not how to use it and when for what projects.

Anonymous at Tue, 4 Jun 2024 11:22:28 UTC No. 16209578

>>16209571
no my point is you need a lot of maturing to actually get an idea what and why laplace/fourirer does without it just being handwaving

saying
>it solves equations
>it transforms from time to frequency
is just repeating some canned answer and does not feel satisfying

Anonymous at Tue, 4 Jun 2024 14:55:36 UTC No. 16209842

>>16209578
NTA but I agree and disagree somewhat.

When you say
> no my point is you need a lot of maturing to actually get an idea what and why laplace/fourirer does without it just being handwaving
You are definitely correct, but I also don't think it's necessarily required to teach the subject at its most serious level of depth to everyone all at once.

Think about how you learned linear algebra. If you went to a somewhat normal university, your first exposure to linear algebra was probably in either a calculus class, or a computation/application oriented linear algebra course fairly early on in your education. You likely learned the basics of matrix algebra and operations, as well as the beginnings of eigenvector/eigenvalue analysis, determinants and traces, vector spaces and projections.

This is not taught to a particularly rigorous or "complete" level of complexity, but it was good enough to teach you the linear algebra foundations you needed for other courses. Then, you may have taken an undergraduate level proof based linear algebra course, where the emphasis was instead looking at linear algebra as a transformation/mapping and the consequences of this view of the subject (product spaces, commutative rings, all of that jazz).

Then, if you go to graduate school, you may have taken a graduate level linear algebra which looks at things at an even higher level of abstraction. You may have learned about layers of transformations, dual spaces, homologies etc.

The point being, you never quite get a complete picture in any of these intermediary steps. Not only do you not get a complete picture, but it would be wildly inappropriate for your professors to introduce such nuances and rigor in your first exposures to the topic.

The purpose of a signals and systems course is not to teach you Fourier analysis at a PhD level so you get the "most complete" level of analysis for the subject. The point is to give you a simple and intuitive understanding.

Anonymous at Tue, 4 Jun 2024 15:17:30 UTC No. 16209882

>>16209842
I agree but it feels like the bar for intuition or ground-level knowledge is a few steps up from linear algebra when it comes to fourier/laplace/complex analysis at least for me

Anonymous at Tue, 4 Jun 2024 16:09:59 UTC No. 16209935

>>16209882
I guess it depends on how you want to look at things.

In some sense a characteristic equation is a characteristic equation. Does it really matter whether those characteristic roots correspond to eigenvalues vs. modal exponents for constant coefficient ODE's?

In another sense, I don't think I really "got" the Laplace transform until I took a complex functions course and learned about Cauchy integration. I don't know if I would have "gotten" Cauchy integration if I wasn't already fairly comfortable with the Fourier and Laplace transforms from a "plug and chug" perspective. Hard to tell really.

Anonymous at Tue, 4 Jun 2024 16:21:18 UTC No. 16209957

>>16203852
People in this thread who explain it as a means of converting ODE into a linear equation are low IQ. Those who explain this as a way to represent a signal as a combination of exponentially growing and decaying oscillations are midwit.

Anonymous at Tue, 4 Jun 2024 16:23:17 UTC No. 16209963

>>16203852
It's a tool for solving differential equations.
What are you, an engineer?

Anonymous at Tue, 4 Jun 2024 16:36:43 UTC No. 16209983

>>16209957
Thank you for your valuable contribution.