
Applied Math Applied Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 9th, 2016, 12:27 PM  #1 
Newbie Joined: Nov 2016 From: South Africa Posts: 2 Thanks: 0  Even and odd periodic extensions
Consider the piecewise function, $f(x)=\left\{\begin{array}{rr}x+4 & 0 < x < 2\\0 & 2 < x < 3\\\end{array}\right\}$  The odd periodic extension $F^O (x)$ of $f(x)$ is defined as: $F^O (x)=\left\{\begin{array}{rr}0 & 3 < x < 2\\x4 & 2 < x < 0\\x+4 & 0 < x < 2\\0 & 2 < x < 3\\\end{array}\right\}$ where $F^O (x)$ has a period of 6.  The odd periodic extension $F^O (x)$ of $f(x)$ is defined as: $F^e (x)=\left\{\begin{array}{rr}0 & 3 < x < 2\\x+4 & 2 < x < 0\\x+4 & 0 < x < 2\\0 & 2 < x < 3\\\end{array}\right\}$ where $F^e (x)$ has a period of 6.  Does the notation used expressions $F^O (x)$ and $F^e (x)$ represent periodic extensions of $f (x)$ that repeats indefinitely every six units? What other notation can be used to present a periodic function of a piecewise function? 
November 9th, 2016, 02:49 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,136 Thanks: 468 
By definition a periodic expression of period 6 repeats every 6 units. The notation you use is as good as any.


Tags 
extensions, odd, periodic 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
isomorphic normal extensions  Epsilon90  Abstract Algebra  4  November 28th, 2013 02:49 AM 
A couple questions regarding field extensions:  declan  Abstract Algebra  5  May 7th, 2010 07:54 AM 
field extensions  shakeydakey  Abstract Algebra  1  October 27th, 2009 11:15 AM 
periodic/not periodic functions application to electronics  conradtsmith  Calculus  1  August 20th, 2009 04:36 AM 
Cyclic Extensions....  TTB3  Abstract Algebra  0  April 2nd, 2009 10:41 AM 