Stanford Research Systems SR785, Руководство по эксплуатации и программированию

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2-8 FFT Frequency Spans
SR785 Dynamic Signal Analyzer
FFT Frequency Spans
Full Span
Full span is the widest frequency span corresponding to the fastest available sampling
rate. In the SR785, this is DC to 131 kHz using a sampling rate of 262 kHz. Because the
signal passes through an anti-aliasing filter at the input, the entire frequency span is not
useable. The filter has a flat response from DC to 102.4 kHz and then rolls off steeply
from 102.4 kHz to 156 kHz. The range between 102.4 kHz and 131 kHz is therefore not
useable and the actual displayed frequency span stops at 102.4 kHz. There is also a
frequency bin labeled 0 Hz (or DC). For a time record of 1024 samples (3.9 ms), this bin
actually covers the range from 0 Hz to 128 Hz (the lowest measurable frequency) and
contains the signal components whose period is longer than the time record (not only
DC). So our final displayed spectrum contains 401 frequency bins. The first covers 0 -
128 Hz, the second 128 - 384 Hz, and the 401st covers 102.272 - 102.528 kHz.
Spans Less Than Full Span
The duration of the time record determines the resolution of the spectrum. What happens
if we want a resolution better than 256 Hz? We need to increase the duration of the time
record. There are two ways to do this - take more points in each time record or lower the
sampling rate. Taking more points is difficult since both the memory and processing
requirements increase with the number of points. The longest time record the SR785 can
process is 2048 points (800 point FFT).
Instead, we take the approach of lowering the sample rate and making the same number
of samples cover a longer time. If we halve the sample rate, this doubles the time record
duration and gives us better resolution. However, the sample rate also determines the
frequency span. By halving the sample rate, we also halve the frequency span. At a
constant number of points in the FFT, we must tradeoff better resolution with narrower
frequency spans.
Changing the sample rate of the A-D converter is not practical since that requires
changing the analog anti-aliasing filter cutoff frequency. Instead, the incoming data
samples (at 262 kHz) are digitally filtered and down-sampled. The advantage is that the
digital filter's cutoff frequency can be easily changed. For example, to decrease the
sampling rate from 262 kHz to 131 kHz, the incoming data is low-pass filtered to remove
any signals above 51.2 kHz. This filter rolls off steeply from 51.2 kHz to 65.6 kHz. Since
output of this filter only contains frequencies up to 65.6 kHz, Nyquist only requires a
sample rate of 131 kHz and only every other point is kept as part of the time record. The
result is a time record of 1024 points sampled at 131 kHz to make up an 7.8 ms record.
The FFT processor operates on a constant number of points and the resulting FFT will
yield 400 bins from DC to 51.2 kHz. The resolution or linewidth is 128 Hz (1/7.8 ms).
This process of halving the sample rate and span can be repeated by using multiple
stages of digital filtering. The SR785 can process a 400 bin spectra with a span of only
195.3 mHz and a time record of 2048 seconds if you have the patience. However, this
filtering process only yields baseband measurements (frequency spans which start at
DC).