2/26/08 Discrete time fourier series x[n] = sum>(Dre^(jrOMEGAn)) x[n] must be No periodic Dr=(1/No)*sum>(x[n]e^(-jrOMEGAn)) ex x[n] = cos(n*pi/10) -> OMEGA = pi/10 -> No = m2pi/OMEGA = m20 -> No=20 x[n] = sum>(Dre^(jpirn/10)) Dr = (1/20)*sum>(x[n]e^(-jrnpi/10)) = (1/40)sum>(e^((1-r)jpin/10)+e^((r+1)(-jpin/10))) D1 = (geometric series) -> = 1/2 example (Fig1) example (Fig2)