2/21/08
midterm solutions! (Fig1)

read 10.1,10.2 homework is 10.1,2,7,8

fourier series
Continuous Time	x(t)=sum<n=-inf,inf>(Dne^(jwnt))	x must be periodic with w as the period
Discrete Time	x[n]=sum<r=-inf,inf>(Dne^(jrOMEGAn)) x must be periodic with period No, OMEGA = 2pi/No
OMEGA=wT
can shift r by No and make no difference on the result so there are only No unique terms
changes equation to x[n]=sum<r=0,No-1>(Dne^(jrOMEGAn))

Dn = sum<r=0,No-1>(x[n]e(-jrOMEGAn)) = sum<n=0,No-1>(Dnsum<r=0,No-1>(e^(j(r-m)OMEGAn)))
if r-m = 0, ans is No
if r-m!=0, its a geometric series since the value can never be greater than 1, so
sum<n=0,No-1>(e^(j(r-m)OMEGA)^n) = (e^(j2pi(r-m))-1) / (e^(j(r-m)OMEGA)-1) = 0
Dm = 1/No *sum<n=0,No-1>(x[n]e^(-jmOMEGAn))

example (Fig2)