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Chapter 6
Advanced Concepts
NI-DSA Software User Manual
The original frequency span center is then shifted to DC or heterodyned,
this means that the upper half of the span stays positive and the lower half
(below the span center) becomes a set of negative frequencies. The result is
that a span from 0 to 80kHz becomes a span of –40 to 40 kHz. This data
goes through a digital low pass filter which cuts off at ±40 kHz, this
operation results in a ±40 kHz usable span centered at 40 kHz. The
sampling rate needed is then only 102.4 kS/s instead of the original
204.8 kS/s hardware sampling rate defined by the selected baseband of
80kHz, so only every other point of the original span is used. At this point
the original baseband span is represented by a complex time record with
half as many points as the original one, half the sampling rate and therefore
same duration (both the real and imaginary part of this complex record have
half of the original sample rate and half of the original span).
If you keep the hardware sampling rate constant at 204.8 kHz, the NI 45XX
can digitally halve the effective sampling rate by passing the digital
samples through one stage of a decimate-by-2 lowpass filter. Digital
filtering and down-sampling are used to narrow the heterodyned data by
zooming around the heterodyne frequency (the center of the original span).
So while the first filter reduces the sampling rate by half and the number of
samples by splitting the time record in real and imaginary parts, the second
filter cuts off at ±20 kHz reducing the sample rate by 2 again, but not the
number of points. The new record then has twice the original duration and
half of the original span, resulting in a a 40kHz span centered around
40kHz. The time record duration is twice the duration of the full span
time-record. The sample rate is one-fourth of the baseband rate.
Further iterations of this process can reduce the span and provide better
resolution for analysis.
If you pass 2,048 samples (for a 2 KS FFT) at 204.8 kHz through this
decimating filter, the output will be 1,024 samples at 102.4 kHz. Both
records correspond to a 10 ms duration time record, and so the frequency
resolution, or bin width, is 1/10 ms = 100 Hz. Once again, the length of the
time record always determines the frequency resolution of the spectrum.
To make sure the decimating filter is fast and memory efficient, the
alias-free range for narrow spans is reduced from 475 lines to the classical
400 lines per 1,024-point FFT to allow the use of a faster and less sharp
filter, thereby improving performance. As a result of this reduction in range,
the maximum alias free frequency span is 80 kHz for zoom instead of the
95 kHz available for baseband. The resulting span is (400/1,024) × f
that our span for one stage of decimation is (400/1,024) × f
6-10
, so
s
/2 = 40 kHz.
s
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