Sampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Example 1<br />
• Let x a (t)=e -1000|t|<br />
X<br />
∞<br />
0<br />
∞<br />
− jΩt<br />
1000t<br />
− jΩt<br />
−1000t<br />
− jΩt<br />
( jΩ)<br />
= ∫ xa<br />
( t)<br />
e dt = ∫ e e dt + ∫ e e dt<br />
−∞<br />
−∞<br />
0<br />
0.002<br />
=<br />
⎛ Ω ⎞<br />
1+<br />
⎜ ⎟<br />
⎝1000<br />
⎠<br />
a<br />
2<br />
• To evaluate X a (jΩ) numerically, we have to approximate x a (t) by a<br />
finite duration grid sequence x G (m)<br />
• Using the approximation e-5=0, x a (t) can be approximate by a finite<br />
duration signal over -0.005
Change language