Chapter 6
Theory of Analog Operation
PCI-4451/4452/4453/4454 User Manual
6-4
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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. To avoid this, it is important to input to the
sampler only those signals that can be accurately represented—those
whose frequency components all 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-445X includes two stages of anti-alias 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
has an extremely flat frequency response in the bandwidth of interest, and
it has very little phase error.
The analog filter precedes the analog sampler, which operates at 128 times
the selected sample rate (26.2144 MS/s in the case of a 204.8 kS/s sample
rate) and is actually a 1-bit ADC. The 1-bit, 128-times oversampled data
that the analog sampler produces is passed on to a digital antialiasing filter
that is built into the ADC chip. This filter also has extremely flat frequency
response and no phase error, but its roll-off near the cutoff frequency (about
0.493 times the sample rate) is extremely sharp, and the rejection above
0.536 times the sample rate is greater than 85 dB. The output stage of the
digital filter resamples the higher frequency data stream at the output data
rate, producing 16-bit digital samples.
