Have i found a new way to generate a square wave? https://w

>>8495637
Maybe, congratulations. It's useless, but I bet it was all worth it.

>>8495637
Not a new formula by a long shot, but it's always good to discover something yourself

>>8495691
is a retard

>>8495693
no u

>>8495637
Great. Now how do you vary the duty cycle?

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42KB, 545x409px

>>8495899
more fiber

>>8495637
>the period is not 1

Dropped.

>>8495899
not op but trying to find out of this is possible with this setup. probably not how its setup but ill try

>>8496147
Wat?

>>8495637
>>8496372
This is just a logistic function, but composed with a periodic function. It is only as useful as a logistic function.

>>8495637
Wow faggot I'm really impressed, the general expression seems to be a lot easier and simpler than an usual Fourier series. It seems that it converges really fast, congratulations. This is a legit publication, go ahead.

>>8496545
This is why /sci/ hates your engineering filth.

>>8496372
>>8496505

Try it now

https://www.desmos.com/calculator/kdak7fogpj

>>8495637
Pretty neat

>>8496545
Or you can just use a piecewise function or modular arithmetic, you fucking nerd.

>>8495637
Very nice, but the amplitude is half of what it should be

Engineer mathlet here, getting into fourier series. Why can a "square wave" be not perfectly square?
Even if it's infinity close to being square it still isn't "square".

>>8497461
Because straight upward slopes (with derivaate = infinity) aren't possible in anything that is an actual function, as you'd have multiple results for the same value.

>>8497461
you mean gibbs phenomenon? fourier series aren't equal in the point-wise sense, they are equal "almost everywhere" i.e. on all sets of non-zero measure.

>>8497461
>>8497514
That isn't true, the cube root function has an infinite slope at x=0, despite it being defined everywhere. The reason a "square wave" can't be perfectly square is the result of definitions. Typically, people want a square wave to be a continuous line, where the bottom cusps are connected by an unbroken line, to the respective top cusps. However, well-defined functions that vary with respect to x cannot do that. Because people want an actual continuous function to describe their system, they pick faux square-wave functions to do the job, when they could easially design a discontinuous function to do the same thing.

>>8497548
>That isn't true, the cube root function has an infinite slope at x=0
The length of said slope is also 0, so it's not the same case at all.

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>>8497548
>implying real life square waves with sufficient rise times show up continuous without interpolation between samples
>implying x^3 is not differentiable on its entire domain

>>8497514
>>8497607
Re read that post
>Because straight upward slopes (with derivative = infinity) aren't possible in anything that is an actual function
the cube root of x is an actual function that has a "straight upward slope (with derivative = infinity)" at x = 0.

>>8497639
>cube root function

I don't think so DESU