The Fourier expansion of a periodic function F(x) with period 2x is given by
[infinity] [infinity]
F(x)=a,+Σan cos(nx)+Σbn sin(nx)
n=1 n=1
where
x
an=1/π∫ f (x) cos(nx)dx
-x
x
ao=1/2π∫ f (x)dx
-x
x
bn=1/π∫ f (x) sin(nx)dx
-x
Consider the following sq
uare wave F(∅) with period 2n, which is defined by
F(∅) = V, 0 <∅<π
-V, π<∅,2π
where F(∅) = F (∅ + 2π)
(a) Sketch this square wave on a well-labelled figure.
(b) Expand F(8) as a Fourier series
(c) What is F(nn)? Show these values on your sketch. (5 marks) (15 marks) (5 marks)