A generalization problem. Help me!

[nkd0808]

Hi everyone,

 

I am now working on a project, in which I use a kind of pulse functions as shown in the figures below ( I call them the 3rd, 4th and 5th models). I have spent about 1 month to mathematically generalize the function (the nth order model). However my mathematical background is not good, so I feel unable to do that though I can graphically draw the models for higher order (6th, 7th, ... order). I am now so worried about the problem because the deadline of the project is approaching.

 

So can someone please help me?

Thank you so much.

 

the 3rd order model (the horizontal axis is time, and the vertical one is manitude)

 

the 4th order model

 

the 5th order model

[Klaynos]

If this is an infinite periodic structure you'll be wanting to use a mathematical method called the fourier series:

 

http://en.wikipedia.org/wiki/Fourier_series

 

This will create a genrallised function, which is an infinite sum of cos and sin terms, the more of this series you use the closer your generalisation to the square function your result will be...