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SAMPLED DATA SYSTEMS
C) SAMPLED ANALOG/DIGITAL SYSTEM
Figure 2·1. Sampled Data System
Figure 2·2. Elements of a Sampled Data System
2.2 Effects of Sampling
Assuming an input spectrum F(jw) and a sampling fre-
quency fs, the output spectrum for square-topped
sampling Fst (jw) is found to be
FST
(jw)
=.2....
sin
(wtl2)
T
wtl2
L
F [j(w-nws)]
n=-oo
From this equation, the gain is a continuous function of
frequency defined by
~
SIn
Jt~y2)
where
T
is the sample
pulse width, t is time, T the sample period, and
w
the
frequency in radians per second.
The time-and-frequency-domain plots for the square-
topped sampled signals are shown in Figure 2-3. Figure
2-3a and 2-3b show the signal before and after sam-
pling. The corresponding spectra are shown in Figure
2-3c and 2-3d respectively. Figure 2-3d is a plot of the
above equations where multiple spectra are formed
around mUltiples of the sample frequency. As long as
2-2
the adjacent spectra do not overlay excessively (aliasing
distortion), the continuous signal can be represented by
discrete samples at that sampling frequency.
The quality of representation of a continuous signal by
the sampled and digitized signal is determined by several
factors: a) sampling rate b) sampling pulse width
c) sampling stability and d) digitizing accuracy. The cor-
responding distortion terms are: a) aliasing noise b)
signal reconstruction noise c) jitter noise and d) quan-
tization noise respectively. These four factors can cause
unacceptable distortion if they are not chosen properly.
By properly designing the sampled data system, these
distortion or noise terms can be made insignificantly
small, so that the sampled data system closely represents
the analog equivalent system.
The sampled data system implementation will have the
added advantages of digital processing and software
flexibility. The following sections will discuss these
sources of imprecision.
a
lnput~slgnal
waveform
b
Square-topped sampled signal
FREQUENCY
c
Input-signal spectrum
{T--;;;;t2
D..
- __
~
::E
..:
~....
--
....
--
t'""""t
•
d
Square-topped sampled-signal spectrum
Figure 2·3. Analysis of Sampled Signal
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