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C
Cornel19-Tanzanite
19-Tanzanite
June 4, 2024
Solved

Pulse function using Heaviside Step Function

  • June 4, 2024
  • 2 replies
  • 3211 views

Hi,

How can I make this pulse like function in more compact way but still following this variant from below?

Cornel_0-1717487481144.png

Cornel_1-1717487492107.png

Best answer by Werner_E

Looks like "laplace" can't deal with "mod", floor" and similar functions and so it can't give you a result for the piecewise and periodic function.

Werner_E_0-1717500610032.png

 

"laplace" can deal with a finite number of pulses, but even then it can't deal with the number of pulses being a variable and not a constant.

Werner_E_1-1717500786669.png

 

I guess that unless PTC implements some kind of rect(t) or SquareWave(t) function and tells the symbolics its laplace transform, we can't talk Prime into returning the result

Werner_E_0-1717501906874.png

which you may expect for your square wave.

-> LaplaceTransform (1/2*SquareWave(t/4)+1/2) - Wolfram|Alpha

-> [Solved] The Laplace transform of the causal periodic square wave of

-> integration - Laplace transform of a square wave function - Mathematics Stack Exchange

2 replies

A
AlanStevens19-Tanzanite
19-Tanzanite
June 4, 2024

Something like this?

Steps.png

 

Alan

C
Cornel19-TanzaniteAuthor
19-Tanzanite
June 4, 2024

Hm, its a good variant also your variant. Idea is with the above variant we can do:

1. Laplace:

Cornel_0-1717488845317.png

Cornel_1-1717488854203.png

Cornel_2-1717488884057.png

 

 

2. Then I will want to extend (if possible) to such waveforms, but still using heaviside step function (and also those waveforms needs to have laplace transform counterpart:

Cornel_3-1717488940860.png

 

I do not know how my variant could look like, maybe something like this:

Cornel_5-1717489191469.png

or maybe splitted in 2 parts, do not know:

Cornel_0-1717489652893.png

 

A
AlanStevens19-Tanzanite
19-Tanzanite
June 4, 2024

Unfortunately, I only have the Express version of Prime, in which there are no symbolics (hence no Laplace), so I'm unable to help you further, I'm afraid.

 

Alan 

W
Werner_E25-Diamond IAnswer
25-Diamond I
June 4, 2024

Looks like "laplace" can't deal with "mod", floor" and similar functions and so it can't give you a result for the piecewise and periodic function.

Werner_E_0-1717500610032.png

 

"laplace" can deal with a finite number of pulses, but even then it can't deal with the number of pulses being a variable and not a constant.

Werner_E_1-1717500786669.png

 

I guess that unless PTC implements some kind of rect(t) or SquareWave(t) function and tells the symbolics its laplace transform, we can't talk Prime into returning the result

Werner_E_0-1717501906874.png

which you may expect for your square wave.

-> LaplaceTransform (1/2*SquareWave(t/4)+1/2) - Wolfram|Alpha

-> [Solved] The Laplace transform of the causal periodic square wave of

-> integration - Laplace transform of a square wave function - Mathematics Stack Exchange

C
Cornel19-TanzaniteAuthor
19-Tanzanite
June 4, 2024

Ok, its good also like this with finite number at this moment :

Cornel_0-1717502197815.png


Now, how to make something like above f(t,n) for these kind of waveforms but using only heaviside step function:

Cornel_1-1717502255835.png

 

W
Werner_E25-Diamond I
25-Diamond I
June 4, 2024
Now, how to make something like above f(t,n) for these kind of waveforms but using only heaviside step function:

Maybe that way:

Werner_E_0-1717506374694.png

 

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