Pulse function using Heaviside Step Function

[Cornel]

Hi,

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

[AlanStevens]

Something like this?

Alan

[Cornel]

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

1. Laplace:

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:

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

or maybe splitted in 2 parts, do not know:

[AlanStevens]

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 

[Werner_E · Accepted solution]

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.

"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.

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

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

[Cornel]

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

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

[Werner_E]

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

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Maybe that way:

[Cornel]

There is this ramp function:

But this function cannot be laplace transform evaluated:

I am wondering if this ramp function can be made in another way and in such a way that laplace transform could be caluculated for it?

EDIT: ok, I found how to do it

[Werner_E]

Laplace assumes f(t)=0 for t<0 anyway, so you could achieve the result easier with

But your picture (red plot)  doesn't show an infinite ramp but rather a triangle impulse ...

[Cornel]

How to make f2(t) to have more numbers of triangles?

[Werner_E]

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@Cornel wrote:

How to make f2(t) to have more numbers of triangles?

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Use the function I posted here
Solved: Re: Pulse function using Heaviside Step Function

with T/2 as second argument (see the second, blue plot).

[ttokoro]