EE511 Day 11 Class Notes
Sampling Theory
Laurence Hassebrook
Updated 9-19-03
Friday 9-19-03
SAMPLING THEORY
Sampling theory gives us the analysis tools for sampling a continuous time signal and from these
samples, reconstruct the original signal.
Consider the cardinal series


wt    an Sa f s  t  n  
f
s

 
n
where
an  f s

 wt Sa f


s
 t  n  dt

f s  

and fs is the sampling rate.
Given Ts = 1/ fs is the sampling period and B is the bandwidth of w(t) s.t.
none zero
f s  2B
If W  f   
and fs>2B
0
else
where

Then an = w(n/fs) = w(nTs).


It can be shown that  n t   Sa f s  t  n   , form an orthogonal set. (draw a couple components)
f
s 
 
There are several types of sampling techniques. They include “impulse”, “natural” and “flat top”
sampling.
IMPULSE SAMPLING
Reconstruction
Practical configuration of impulse sampling
NYQUIST SAMPLING RATE AND ALIASING
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