Quick Periodic Extension Question

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

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

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.

In the general case (on the real line) for your function $\displaystyle k \in \mathbb{Z}$