Stanford Research Systems SR785, Руководство по эксплуатации и программированию

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2-10 FFT Time Record
SR785 Dynamic Signal Analyzer
FFT Time Record
The FFT operates on time records. A time record is simply a sequence of data samples.
The duration of the time record is the FFT resolution/span. There are two types of time
records, those corresponding to baseband spans (starting at DC) and those corresponding
to zoomed spans (not starting at DC). Zoomed time records are heterodyned (frequency
shifted) and do NOT contain the input signal at its original frequencies.
Baseband Time Records
Baseband time records are very simple to understand. They represent the input signal
passed through low-pass filters. At full span, the signal has passed through the analog
anti-aliasing filter. The sample rate is 262 kHz. To get the time records for narrower
spans, the data is digitally filtered and down-sampled. At a given FFT resolution, each
time the span is halved, the bandwidth of the time record is halved and the sampling rate
is halved. The length of the time record (in seconds) doubles.
Heterodyned Time Records
Zoomed time records are more complicated. Heterodyning is a complex operation. The
input points are multiplied by cos(
ω
t) and sin(
ω
t) to yield a real and an imaginary part.
ω
is 2
π
times the span center frequency. The real and imaginary parts of each point are
orthogonal. You can think of the complex time record as two separate records, one real
and one imaginary.
The input signal is frequency shifted or heterodyned. This moves signals at the span
center to DC and frequencies below span center to negative frequencies. If the span
center is at 51.2 kHz, the input range from 0 to 102.4 kHz is shifted to -51.2 kHz to
+51.2 kHz. This data is then passed through a low-pass filter which cuts off at
±
51.2
kHz. This results in a ±51.2 kHz (102.4 kHz) useable span centered at 51.2 kHz. The
output data only requires a sampling rate of 131 kHz (instead of the original 262 kHz real
input rate) so only every other point is saved. Thus, the original 102.4 kHz span is
represented by a time record with half as many points and half the sampling rate and the
same duration. How can this be?
The complex time record has half as many points as the baseband (real) time record with
the same span and resolution. This is because the negative frequency part of the spectrum
is kept in the heterodyned case. You can think of the real and imaginary parts of the
complex time record as completely independent data streams, each at half of the original
sample rate and each with half of the original span. Together, they represent the original
span with the original number of samples and the original time record length.
Digital filtering and down-sampling is used to narrow the span of the heterodyned data.
This ‘zooms’ in around the heterodyne frequency (span center). The first digital filter
reduces the sample rate by 2 (to 131 kHz) but does not reduce the span.
The second digital filter cuts off at ±25.6 kHz and reduces the sample rate by 2 again.
The number of points in the time record is NOT halved again (this only happens at the
first filter due to the splitting of the real time record into two parts, real and imaginary).
The new time record must have twice the original duration and thus, half of the original
span. This results in a 51.2 kHz (±25.6 kHz) span centered at 51.2 kHz. The time record