Revision as of 05:40, 25 September 2008 by Phscheff (Talk)

Fourier Transform

Let $ x(t)=sin(\pi t) + cos(2\pi t) $

Remember that the formula for CT Fourier Series are:

$ x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t} $

$ a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt $.

Solution

$ x(t)= \frac{e^{\pi jt}+e^{-\pi jt}}{2j} + \frac{e^{2\pi jt}+e^{-2\pi jt}}{2} $

$ \omega_0 = \pi $

$ a_1=\frac{1}{2j} $

$ a_2=\frac{1}{2} $

else $ a_k $ equals 0

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang