Math question

[Pandamonium]

My GF's the one trying to figure this out, and I have no clue. (I was basically done with math after calc3.)

The function looks like this:
/\/\/\/\/\/\/

Where the minima are at y=0. I thought at first it would involve abs() because the function never went below zero. Then I realized that abs() doesn't address the fact that the lines meet at a point.

It's supposed to be a function that can be integrated, because it's part of a fourier series. I have no clue how they work, but I figure someone here might =P

Edit: apparently it's for a fourier series and not a fourier transform.

 

[Saint Michael]

What class is this for?

 

[Pandamonium]

"Signals and Systems" - under systems engineering.

 

[BrownTown]

Thats just a triangle wave, what are your trying to get from it?, the Fourier transform of the function can be obtained by Google in about 10 seconds, if you are looking for a nice formula like "Y=something" then I for one don't know of one nor do I think one exists.

EDIT: yep, definitely cannot find a question anywhere in your post...

 

[Pandamonium]

She's looking for the y=something function so that she can integrate it. This is a question on one of the practice exams. Apparently she needs to integrate a function in order to get an answer, but we're stuck at the identify the function step.

 

[BrownTown]

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

Just remember your triangle wave has a DC offset applied to it as well to get its minimums at 0 and not -1. Obviously there are scaling factors there to vary its period and amplitude as well as offset all in the equation given.

EDIT: additionally, the integral will obviously approach infinity in some sort of sinusoidal stairstep fashion.

 

[chuckywang]

Originally posted by: BrownTown
http://en.wikipedia.org/wiki/Triangle_wave

Just remember your triangle wave has a DC offset applied to it as well to get its minimums at 0 and not -1. Obviously there are scaling factors there to vary its period and amplitude as well as offset all in the equation given.

It's quite some work to derive that however.

 

[BrownTown]

Originally posted by: chuckywang

Originally posted by: BrownTown
http://en.wikipedia.org/wiki/Triangle_wave

Just remember your triangle wave has a DC offset applied to it as well to get its minimums at 0 and not -1. Obviously there are scaling factors there to vary its period and amplitude as well as offset all in the equation given.

It's quite some work to derive that however.

I'm not entirely sure that is true, the integration operator is linear, so integrating over and infinite some of sinusoids can be done by taking the infinite sum of the integrals of these sinusoids, all you have to go is just integrate that one function and you have the answer in sigma notation. Additionally so far as numerical accuracy is concerned the amplitude of the harmonics is falling off at the square of their number so you can pretty much just ignore anything past the first four. Additionally, a computer program like MATHEMATICA could calculate it any way you want it in the blink of an eye.

 

[SpecialEd]

Just define the function piece-wise using the greatest integer function |_x_|:

Let f(x)=x-|_x_| if |_x_| is even

and

f(x) = 1-x+|_x_| if |_x_| is odd


This fucntion will just be the lines y=x and y=1-x on [0,1] repeated over and over.