Intel 2920 Design Handbook page 18

SAMPLED DATA SYSTEMS
2.2.1 Aliasing Noise
A sampling theorem relating the minimum required
sampling frequency
to
the signal bandwidth can be
stated as follows: if a signal f(t), a real function of time,
is sampled instantaneously at regular intervals, at a rate
higher than twice the signal bandwidth, then the
sampled signal contains all the significant information
of the original signal. This would then define the
minimum sampling frequency required. In practice, a
sampling rate of 3 to 4 times the 3dB bandwidth of the
input signal is not uncommom.
Figure 2-4 shows the effects of sampling rate on the
separation of sampled signal spectra. When the sample
rate is
r~duced,
the adjacent spectra overlaps. The
TIME DOMAIN
AM'~'C7L
TIME
A·'I~LLL:/
TIME
A·'I~
TIME
A. ' )
~
TIME
overlapped spectral energy cannot be separated from
the desired signal and so a distortion is caused called
aliasing noise.
Figure 2-4 shows the effect of sample rate on aliasing
noise for a given input signal. Note the amount of
overlap increases as the sampling frequency is decreased
for a fixed input signal bandwidth. Similarly, for a fixed
sampling frequency, the overlap could be reduced by
increasing the frequency. The overlap couJd also be
reduced by increasing the frequency rolloff of the input
signal by using anti-aliasing filters prior to sampling.
Figure 2-5 illustrates the overlap for several types of
popular anti-aliasing filters. These tradeoffs between
filter selectivity and sampling frequency are part of the
design process with sampled data systems. Such trade-
offs are discussed more fully in later chapters.
FREQUENCY DOMAIN
A. ' I
~
FREQ
A. ' I
f. FREQ
AMP
f.
FREQ
A·'IZ!.
\
•
FREQ
Figure 2-4. Effects of Sampling Rate on Aliasing Noise
2-3