Quick Periodic Extension Question

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• September 26th 2009, 03:44 PM
BlackBlaze
Quick Periodic Extension Question
If you were asked to do a periodic extension of a function and to increase the period, would you stretch the parameters out?

For example:
$f(x)=\left\{\begin{array}{cc}x^2,&\mbox{ if }
[0,1)\\2-x, & \mbox{ if } [1,2]\end{array}\right.$

If were told to do a periodic extension, but change the period from 2 to 4, how would I go about doing this? Would I change the first interval from [0,1) to [0,2)?
• September 26th 2009, 05:05 PM
DeMath
Quote:

Originally Posted by BlackBlaze
If you were asked to do a periodic extension of a function and to increase the period, would you stretch the parameters out?

For example:
$f(x)=\left\{\begin{array}{cc}x^2,&\mbox{ if }
[0,1)\\2-x, & \mbox{ if } [1,2]\end{array}\right.$

If were told to do a periodic extension, but change the period from 2 to 4, how would I go about doing this? Would I change the first interval from [0,1) to [0,2)?

Look closely this picture.

http://s52.radikal.ru/i137/0909/2d/30a4c2b1447c.png

I think that is understandable.

In the general case (on the real line) for your function $k \in \mathbb{Z}$
• September 27th 2009, 12:09 PM
BlackBlaze
Wait.
Wait, wait, wait, wait.

...Nope, I lost it. Forgive me, I guess I'm not that bright. I see you were able to make a simple periodic extension of my function, but I do not understand how the k plays a part. Am I to extend function so that when k = 0, f(x) can go across 0->4?