(→A periodic CT signal) |
(→A periodic CT signal) |
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Input CT signal: <math> x(t) = cos2t+sin2t</math> | Input CT signal: <math> x(t) = cos2t+sin2t</math> | ||
| − | <math>\,x(t)={e^{2j\pi t}+e^{-2j \pi t}}{2} + {e^{j2 \pi t}-e^{-j2 \pi t}}{2j}</math> | + | <math>\,x(t)=\frac {e^{2j\pi t}+e^{-2j \pi t}}{2} + \frac {e^{j2 \pi t}-e^{-j2 \pi t}}{2j}</math> |
| + | |||
<math>x(t)=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)=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> | ||
Revision as of 15:19, 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)=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} $
