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Chapter 6 Theory of Analog Operation
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National Instruments Corporation 6-3 PCI-4451/4452 User Manual
Antialias Filtering
A sampling system (such as an ADC) can represent signals of only limited
bandwidth. Specifically, a sampling rate of F
s
can only represent signals
with a maximum frequency of F
s
/2. This maximum frequency is known as
the Nyquist frequency. If a signal is input to the sampling system with
frequency components that exceed the Nyquist frequency, the sampler
cannot distinguish these parts of the signal from some signals with
frequency components less than the Nyquist frequency.
For example, suppose a sampler (such as an ADC) is sampling at 1,000 S/s.
If a 400 Hz sine wave is input, then the resulting samples accurately
represent a 400 Hz sine wave. However, if a 600 Hz sine wave is input, the
resulting samples again appear to represent a 400 Hz sine wave because this
signal exceeds the Nyquist frequency (500 Hz) by 100 Hz. In fact, any sine
wave with a frequency greater than 500 Hz that is input is represented
incorrectly as a signal between 0 and 500 Hz. The apparent frequency of
this sine wave is the absolute value of the difference between the frequency
of the input signal and the closest integer multiple of 1,000 Hz (the
sampling rate). Therefore, if a 2,325 Hz sine wave is input, its apparent
frequency is:
2,325 − (2)(1,000) = 325 Hz.
If a 3,975 Hz sine wave is input, its apparent frequency is:
(4)(1,000) − 3,975 = 25 Hz.
The process by which the sampler modulates these higher frequency
signals back into the 0 to 500 Hz baseband is called aliasing.
If the signal in the previous example is not a sine wave, the signal can have
many components (harmonics) that lie above the Nyquist frequency. If
present, these harmonics are erroneously aliased back into the baseband
and added to the parts of the signal that are sampled accurately, producing
a distorted sampled data set. Input to the sampler only those signals that can
be accurately represented. All frequency components of such signals lie
below the Nyquist frequency. To make sure that only those signals go into
the sampler, a lowpass filter is applied to signals before they reach the
sampler. The PCI-4451/4452 has complete antialiasing filters.
The PCI-4451/4452 includes two stages of antialias filtering in each input
channel lowpass filter. This filter has a cutoff frequency of about 4 MHz
and a rejection of greater than 40 dB at 20 MHz. Because its cutoff
frequency is significantly higher than the data sample rate, the analog filter
User.book Page 3 Tuesday, April 14, 1998 10:20 AM