Could you please post your book's definition of the Fourier Series? There are different conventions about multiplying constants out in front, as you go from book to book.
Hi,
I was recently doing some revision and encountered a slight problem with my an calculation for the fourier series..
heres the problem
f(x)=0 -pi<x<-pi/2
f(x)=4 -pi/2<x<pi/2
f(x)=0 pi/2<x<pi
f(x)=f(x+2*pi)
consider one cycle between x=-pi and x=pi
when i calculated the an, I got 8/(pi*n) but in the textbook it says 8/(pi*n)sin(n*pi)/2 so could someone explain how the sin(n*pi)/2 came about?? Your help would be much appreciated..
Hi,
actually an=(8/pi*n)sin(n*pi)/2 thats what the Advanced Engineering Math A by K.A STROUD says, however the sin(n*pi)/2 term is not zero for all integers.
for example if n is even an=0
If n=1,5,9,.. an=8/(n*pi)
If n=3,7,11,... an= -8/(n*pi)
I'm confused about how the sin(n*pi)/2 term came about..any information is welcome..thank you
... the following expansion of , the coefficients are given by , for , and , for .
Now, the function you've given is even. Hence, all the 's vanish. The integral for the 's looks like the following:
.
This, in turn, implies
.
Now this explains the existence of the term, I hope. This expression can be simplified even further if you evaluate the trig function at the specified points: the even integer multiples vanish, and the odd integer multiples look like powers of .
Hope this helps.