(The Inverse Fourier Transform)
(The Inverse Fourier Transform)
Line 12: Line 12:
 
<math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(j \omega)e^{j\omega t}d\omega</math>
 
<math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(j \omega)e^{j\omega t}d\omega</math>
  
 +
For this problem I will not be using the above equation but in stead be using duality.
  
<math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\cos(4 \omega + \frac{\pi}{3})e^{j\omega t}d\omega</math>
+
<math>x(t) = \cos</math>
 
+
 
+
<math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\frac{ e^{j(4 \omega + \frac{\pi}{3})} + e^{-j(4 \omega + \frac{\pi}{3})}}{2}e^{j\omega t}d\omega</math>
+
 
+
I do not know how to go from here because I believe it would go to Infinity. I will visit Mimi to find out what to do.
+

Revision as of 10:12, 8 October 2008

The Signal

$ X(j \omega) = \cos(4 \omega + \frac{\pi}{3}) $

Taken from 4.22.b from the course book, it looks interesting and I want to try it.


The Inverse Fourier Transform

$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(j \omega)e^{j\omega t}d\omega $

For this problem I will not be using the above equation but in stead be using duality.

$ x(t) = \cos $

Alumni Liaison

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

Buyue Zhang