(A periodic CT signal)
(A periodic CT signal)
Line 16: Line 16:
  
  
<math>x(t)=\frac{1}{2}e^{j\pi t}+\frac{1+j}{2}e^{-j\pi t}+\frac{1+j}{2j}e^{j2\pi t}+\frac{-1-j}{2j}e^{-j2\pi t}</math>
+
<math>x(t)=\frac{1}{2}e^{j\pi t}+\frac{1}{2}e^{-j\pi t}+\frac{1}{2j}e^{j2\pi t}+\frac{-1}{2j}e^{-j2\pi t}</math>

Revision as of 15:20, 26 September 2008

A periodic CT signal

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

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


Input CT signal: $ x(t) = cos2t+sin2t $

$ \,x(t)=\frac {e^{2j\pi t}+e^{-2j \pi t}}{2} + \frac {e^{j2 \pi t}-e^{-j2 \pi t}}{2j} $


$ x(t)=\frac{1}{2}e^{j\pi t}+\frac{1}{2}e^{-j\pi t}+\frac{1}{2j}e^{j2\pi t}+\frac{-1}{2j}e^{-j2\pi t} $

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva