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SAM PLED DATA SYSTEMS
10
20
30
40
1/21s
FREQUENCY
o
0
3 POLE BWRTH
.0
3POLEO 3dBTCH
A
0
5 POLE BWRTH
. .
0
5POLEO 3dBTCH
c
0
7 POLE BWRTH
•
0
7POLEO 3dBTCH
Is
Figure 2·5. Effects of Filtering on Aliasing Noise
2.2.2 Signal Reconstruction Distortion
Signal reconstruction is the process that extracts the
desired signal from the periodic output samples which
have been formed after digital processing.
DIGITAL
INPUT
D/A
The intention is to convert the signal, which has been
sampled and held after digital processing, back to
analog form with a minimum loss of information. The
output of a sample-and-hold circuit (S&H) or a digital-
to-analog converter
(DI A) has a frequency spectrum as
shown in Figure 2-6 where the sample width
T
is equal to
the period of the sample T. The amplitude gain factor
has a noticeable rolloff within the signal bandwidth
when that bandwidth approaches half the sampling fre-
quency. Unless it is compensated for, this distortion of
the input signal will cause loss of information similar to
the loss from a lowpass filter with insufficient band-
width. Table 2-1 lists the rolloff in dB as a function of
the sample width
T
and the signal bandwidth B.
To correct this situation, either the reconstruction
sampling pulse width should be made narrow relative to
one over the signal bandwidth
(1/B),
or a sin(x)/x cor-
rection should be applied in the output filter.
Figure 2-6b shows the effect of resampling with a nar-
rower pulse. The amount of signal energy contained in
the narrower sampling pulses declines by an amount
proportional to the duty cycle
TIT. It may be necessary
to compensate for this gain loss when analyzing the
relative effects of fixed offsets, overshoot, ringing, and
other spurious signals that degrade the desired signal.
ANALOG
OUTPUT
· 1
L
S&H
~
_ _ _
----I,",~I RECO~~L~~~CTION
' -_ _ _ _ _ -" (8)
""--_ _ _ _ _ .... (C)
.;
(A)
AM'I~
LLJ
..
TIME
AMP
I.
FREO
AM' I
n
n Dr-.
(8)
DODD
TIME
AM'
t
~"
I.
FREO
AM'p~//
(C)
-------
RECONSTRUCTION
AMP
,
,/FILTER
,
"
"
I.
FREO
..
TIME
Figure 2-6. Analog Signal Reconstruction
2-4
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