SIGNAL CONDITIONING
ANTI-ALIASING FILTERS REDUCE
ERRORS IN DATA ACQUISITION
Aliasing, the corruption of in-band signals by out-of-band signals during
A/D conversion, is an intrinsic, invisible, and insidious aspect of data
sampling. Low-pass, anti-aliasing filtering prior to A/D conversion is the
only means by which such aliasing may be prevented in
data acquisition for test measurement
// DOUGLAS FIRTH
When analog signals are sampled by
A/D converters, the resultant digital
data record can be corrupted by
signals outside of the bandwidth of interest
such that they cannot be distinguished
from in-band signals. Termed aliasing, the
nature of such potential corruption is that
it is undetectable, as illustrated in Figure 1,
where sampled data points are taken at a
sampling frequency, FS, of 5 kHz. As may be
seen, the sampled data points of the 4 kHz
sine wave are indistinguishable from the
sampled data points of the 1 kHz sine wave.
The only way to prevent the 4 kHz sine
wave from producing an alias at 1 kHz is to
use an analog anti-alias filter to attenuate
the 4 kHz signal at the A/D converter input
as shown in Figure 2.
ALIASES
Two frequencies, f1 and f2, are said to be
aliases of each other if sampled data points
of their corresponding sinusoids cannot be
distinguished. This occurs if there exists a
positive integer, n, such that f1 = nFS ± f2.
Sampled data points of every frequency in
the spectrum, no matter how high, will
have the equivalent sampled data points of
some frequency in the interval from DC to
FS/2. The aliases of a given frequency in the
signal of interest, fa, lying in the interval
from DC to FS/2, are nFS ± fa. The
frequencies in this interval are referred to
as principal aliases and the limit of this
interval FS/2 is termed the Nyquist or
folding frequency.
Aliasing is also referred to as spectrum
170 SHOWCASE 2020 \\ AEROSPACETESTINGINTERNATIONAL.COM
1 // 4 kHz Alias of 1 kHz
Signal at 5 kHz Sample
Rate
2 // Block Diagram of Data
Conversion System
3 // Aliasing as Spectrum
Folding at Multiples of FS/2
4 // Anti-Alias Filter with
Spectrum Folding about
FS/2 (Linear Frequency
Axis)
5 // Comparison of
Low-Pass Filter-Properties
folding because the pattern of aliases
corresponds to the folding up of the
frequency axis. In Figure 3, the frequency
axis is marked off linearly in intervals that
are multiples of the folding frequency. Also
labeled on this axis are a number of
frequencies that are aliases of one another,
fa, fb, fc, … fg, given by nFS ± fa. If the
frequency axis is folded at multiples of FS/2,
then the set of aliases fa, fb, fc, … fg are
superimposed on each other and are
indistinguishable.
ATTENUATION OF ALIASES
Low-pass filtering, in addition to removing
out-of-band energy that could corrupt
in-band data, serves to band-limit the
signal prior to subsequent sampling. The
sampling frequency of the digitizer must
then be set high enough to assure adequate
attenuation of signals that could alias into
the pass-band of the filter.
As discussed above, any frequency
higher than FS/2 will fold into the band
between DC and FS/2. Given this, a lowpass
filter is needed to attenuate such
frequencies to an acceptable level. In
practice, however, the theoretical sampling
frequency must be increased to account for
the fact that actual realizable filters do not
have infinite attenuation slopes. The lowpass
filter in front of the A/D converter
must be set to attenuate signals that will
alias without significantly attenuating the
signal itself.
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