Revision as of 18:03, 25 September 2008 by Han45 (Talk)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Discrete time Fourier series

$ x[n] = \sum_{k=N} a_ke^{-jkw_0n} $

$ a_k = \frac{1}{N}\sum_{n=N} x[n]e^{-jkw_0n} $

assume that

x[0] = 0

x[1] = 2

x[2] = 0

x[3] = 2

x[4] = 0

.

.

.

.


N = 4

let's solve for coefficients

$ w_0 = \frac{2\pi}{4} $

$ a_0 = \frac{1}{4}\sum_{n=0}^{3} x[n]e^{-j0(\pi/2) n} = \frac{1}{4} (0+2+0+2) = 1 $

$ a_1 = \frac{1}{4}\sum_{n=0}^{3} x[n]e^{-j(\pi/2) n} = \frac{1}{4} ((0*1)+(2*-j)+0+(2*-j)) = \frac {-2j}{2} $

Alumni Liaison

has a message for current ECE438 students.

Sean Hu, ECE PhD 2009