How do I find the fourier series approximation to the even extension of g(t), where g(t) is given as shown below using the fact that :
I was thinking that perhaps since the period is 6 that we need to change the intervals so they are equal to something like 0<t<1/2
Alternatively, it may have something to do with the range -3<t<3
In which case the even extensions will be those that have positive y and the odd will have negative y.
Its really difficult - hope someone on this forum can help out with this one.
I think you are right about the range being -3<t<3, as in part a of the question the function f(t)=f(t + 2pi)
2pi was the period of the function, so if you look at the formulas for even and odd extension they use the letter and is defined as the period.
If is equal to 3 as the fundamental interval is then 2x3 equals 6 giving us the desired period...... i think.
Yeah
I think for part i) it is only asking you to write the extensions in function form.
So I have something like
G(odd) (t) =
-1 (-3<= t <-2)
0 (-2<= t < -1)
1 (-1<= t < 0)
then
G(even) (t) =
1 (-3<= t <-2)
0 (-2<= t < -1)
-1 (-1<= t < 0)
Then draw each graph...
Does that make some sense? (sorry i'm still not up to speed on Latex)