🧵 Absolutely based
Anonymous at Fri, 8 Mar 2024 06:54:46 UTC No. 16062426
Name a more based algorithm than the Fourier transform
Anonymous at Fri, 8 Mar 2024 06:56:08 UTC No. 16062428
>>16062426
Imagine integrating over numbers tbat don't exist.
Anonymous at Fri, 8 Mar 2024 07:00:48 UTC No. 16062432
>>16062428
What is it supposed to be complex?.
Anonymous at Fri, 8 Mar 2024 07:01:56 UTC No. 16062437
>>16062426
The Laplace transform.
Fourier transform is just a special case of LT.
https://youtu.be/n2y7n6jw5d0?t=1m
Anonymous at Fri, 8 Mar 2024 07:25:40 UTC No. 16062469
>>16062437
True, seems more useful for structural engineering
Anonymous at Fri, 8 Mar 2024 07:32:02 UTC No. 16062480
>>16062469
The Laplace transform is much more useful for a wide variety of circumstances.
For systems engineering, the Laplace transform gives you the ability to deal with "windowed" signals instead of just a linear combination of Fourier representations with a constant amplitude. This is how modern communications receivers function.
For control, Laplace transforms give you the ability to analyze an LTI system's response to literally any bounded input signal. If your system is able to be linearized at an equilibrium or has some finite bandwidth, you can extend this notion to a whole host of non-linear, time varying systems as well via state transition matrices (which are Laplace transforms in disguise).
The Laplace transform gives you the moment generating function of a continuous probability density. This moment generating function gives you an absurd amount of information about the function, including about its behavior if you were to form a random walk from repeated sampling of this density.
The Laplace transform is so powerful it's kind of mind boggling honestly.
Anonymous at Fri, 8 Mar 2024 07:38:22 UTC No. 16062487
>>16062480
nice thanks
Anonymous at Fri, 8 Mar 2024 08:37:44 UTC No. 16062530
Fourier transform is one of those things convincing me that Platonism must be right.
>some dude tries to express certain functions as superpositions of waves
>seems tedious but somewhat practical
>solution unexpectedly becomes elegant and concise (OP's pic)
>turns out to be even more useful due to its properties, e.g. being unitary and translating differential into algebraic equations
>can be formulated even more beautifully in its generalization to locally compact abelian groups and their Pontryagin duals without losing any of its based properties
>is not just a mathematical tool but fundamental to nature itself, i.e. in quantum mechanics yielding the transformation between position and momentum basis, giving rise to the uncertainty principle
>is one of the fundamental building blocks of quantum computer algorithms allowing for an exponential speedup in cracking hidden subgroup cryptography
This just can't be a coincidence or a purely artificial construct.
Anonymous at Fri, 8 Mar 2024 08:38:30 UTC No. 16062531
>>16062426
>algorithm
TCSD
Anonymous at Fri, 8 Mar 2024 23:03:09 UTC No. 16063769
>>16062426
That's not an algorithm.
The Fast Fourier Transform or FFT is an algorithm, and is the most based algorithm, without which you would not have digital pictures, movies, audio, cell phones... and so on.
Anonymous at Fri, 8 Mar 2024 23:17:56 UTC No. 16063791
Fourier transform is pop-sci tier.
🗑️ Anonymous at Fri, 8 Mar 2024 23:32:52 UTC No. 16063811
Anonymous at Fri, 8 Mar 2024 23:33:10 UTC No. 16063814
>>16063791
spoke the retard on a device that uses it constantly
Anonymous at Sat, 9 Mar 2024 04:55:06 UTC No. 16064391
>>16062530
It isn't just a fundamental building block in quantum computing, it's literally one of the most important concepts in Probability and Stochastic Processes.
If you have a stationary continuous time stochastic process, the Fourier transform of the process gives you the power spectral density. This tells you "how quickly it changes" just like for a deterministic waveform.
Essentially, if your power spectral density is band-limited, you can sample quickly enough that your last sample will be guaranteed to be correlated with your next sample (meaning you can leverage your previous information, or even get an informative average).
Anonymous at Sat, 9 Mar 2024 05:01:34 UTC No. 16064403
>>16063814
no it doesnt, antenna is cyclic physically
Anonymous at Sat, 9 Mar 2024 06:50:40 UTC No. 16064527
>>16062426
>fourier transform
>algorithm
can we please kill all the underages on this fucking board?
Anonymous at Sat, 9 Mar 2024 07:02:29 UTC No. 16064542
>>16064527
standard whiny little faggot contributing nothing to the discussion
Anonymous at Sat, 9 Mar 2024 07:07:20 UTC No. 16064548
>>16062426
The fourier transform is not an algorithm. You must be the nigger that says computer science is mathematics and the programmers need to know real analysis
Anonymous at Sat, 9 Mar 2024 07:07:56 UTC No. 16064550
>>16064542
what discussion? kys
Anonymous at Sat, 9 Mar 2024 08:08:54 UTC No. 16064616
>>16062426
Hadamard transform.
Anonymous at Sat, 9 Mar 2024 09:57:34 UTC No. 16064768
>>16062426
Poisson summation is more based (and more fundamental).
Also, put the 2*pi*i in the exponent you savage. Have some self respect.
Anonymous at Sun, 10 Mar 2024 10:59:15 UTC No. 16066241
when I worked in research we had an algorithm that would take the Laplace transform of a function, do some operations, and then numerically find the Laplace inverse for some points
were we retarded or are there times where this is actually better than just solving the original problem numerically?