RMS of square, sine and triangle waves

[Juan Pablo]

I'm trying to calculate the RMS for square, triangle and sine waves. I can easily do the integrtion for sine waves and for square waves by looking at the graphic and getting the areas. It doesn't seem as easy for triangle waves since its squared form looks much more complicated and I'm not really sure how to calculate the integrals. I appreciate any guidance.

Thanks in advance.

 

[Matterwave]

Do you know how to integrate without graphs? I.e. integrating using the equation for the wave?

 

[Juan Pablo]

Yeah sure, but most of the expressions for triangle waves use strange functions and I'm not sure how I would find the antiderivative of the triangle wave.

 

[Matterwave]

The expressions for a triangle wave should just be a bunch of linear functions next to each other...which will turn into parabolic functions when you square them. What strange functions are you talking about?

For example, a triangle wave may be: y=x for 0<x<1; y=-x+2 for 1<x<3; etc.

 

[Juan Pablo]

I feel like an idiot. I didn't realize I could use a piecewise function. Thanks! In the case of the square wave should I just use the graph for the integral or is there a more elegant way to do it? By strange function I meant the ones here http://en.wikipedia.org/wiki/Triangle_wave

 

[Matterwave]

The function there is a Fourier series expansion of a triangle wave. It's useful for some applications, though not this one particularly. Just use the piecewise definition, it's much easier.

I don't see any reason for the square wave to do any more than look at the area underneath the graph. That is the simplest method, and integrating is doing the same thing.

 

[Juan Pablo]

Thanks again! You really cleared out everything.