Tektronix 2221 - OBSERVING AND REMOVING ALIASES IN STORE MODE; Aliasing and Anti-Aliasing Techniques

Basic
Applications
—
2221
Operators
during the
complete
sine -
wave period ( 20
times
for
2
periods ) , and the waveform will be accurately reproduced .
100
u
30
AN
a
+
4mV
P - P
u
If the input
frequency is
increased beyond 8 MHz
, the
samples will soon become less than two times per period .
This occurs at 10 MHz for a 20 MHZ sample rate . Past
this point , information sampled from two different sine
wave periods would be used to reconstruct the displayed
waveform . Obviously , this waveform could not be a
correct
reproduction of the input
signal . At certain
input
frequencies the
data
sampled would
reproduce what
appears to
be a
correct
display ,
when in fact it
was only
related to the input signal by some multiple or part of a
multiple of the input signal . This type of display is one
type of " alias " ( see Figure 6-24A ) .
to
U
2mV !
4998-25
Figure 6-23 . Low - level signal , AVERAGE mode .
The example
given is for
the maximum
sampling rate
of
20 MHz . However , the sampling rate is controlled by the
SEC / DIV switch , and whenever it is set so that the input
signal is sampled less than 10 times per period of the
fastest frequency component , observable aliases occur .
OBSERVING AND REMOVING
ALIASES IN STORE MODE
90
Aliasing
C
( A ) POSSIBLE
ALIAS
SIGNAL IN STORE MODE
.
This discussion assumes the acquisition mode is set to
SAMPLE . In
digital sampling ,
the
accuracy of
the
repro
duced waveform , when displayed , increases with the
number of samples obtained during one full cycle of the
signal . That is , a more accurate reproduction of a signal is
possible when more samples of the signal are obtained .
The instrument displays 1000 samples across the full 10
horizontal divisions of the graticule when in the STORE
mode . This means that a sine wave spread across the full
screen is sampled 1000 times , but if the sine wave is only
one graticule division in width , it will be sampled one - tenth
as many times
( 100
samples ) . This
number is still ade
quate for accurate reproduction of the stored waveform .
U
( 8 ) NON STORE
DISPLAY
.
90
If the SEC / DIV switch is set so that the entire sine
wave period fills one - tenth of a graticule division , it is sam
pled only 10 times during its acquisition . This means that
only ten samples of the waveform will be available to
reproduce the waveform for display . In theory , if a sine
wave is sampled at least two times during its period , it
may be accurately reproduced . In practice , the sine wave
can be reconstructed , using special filters , from slightly
more
than
two
samples .
u
u
( C ) ALIAS SIGNAL DISPLAY IN ACCPEAK
STORE
MODE
.
4998-26
At 5 us per division , the instrument's SAMPLE mode
has a useful storage bandwidth of 2 MHz and a maximum
sampling rate of 20 MHz . Consequently , a signal at the
upper
frequency limit is
sampled a
minimum of 10
times
u
Figure 6-24 . Anti - aliasing .
6-22
u