Chapter 7 473
Language Reference
FFT Fast Fourier Transform
The FFT algorithm assumes that the sampled signal is periodic with an
integral number of periods within the time-record length (that is, the
sweep time of the analyzer). Given this assumption, the transform
computed is that of a time waveform of infinite duration, formed of
concatenated time records. In actual measurements, the number of
periods of the sampled signal within the time record may not be
integral. In this case, there is a step discontinuity at the intersections of
the concatenated time records in the assumed time waveform of infinite
duration. This step discontinuity causes measurement errors, both
amplitude uncertainty (where the signal level appears to vary with
small changes in frequency) and frequency resolution (due to filter
shape factor and sidelobes). Windows are weighing functions that are
applied to the input data to force the ends of that data smoothly to zero,
thus reducing the step discontinuity and reducing measurement errors.
Three types of windows are available, using the TWNDOW command.
FLATTOP provides optimum amplitude accuracy.
HANNING provides an amplitude accuracy and frequency
resolution compromise, which is useful for general
purpose measurements, as well as noise
measurements.
UNIFORM provides equal weighing of the time record for
measuring transients.
Some important parameters of the three available windows are shown
in the table below. In the bandwidth entries, multiply the entry by
one-divided-by-sweeptime (1/sweeptime).
FLATTOP HANNING UNIFORM
Noise equivalent bandwidth 3.63× 1.5× 1×
3 dB bandwidth 3.60× 1.48× 1×
Sidelobe height <−90 dB −32 dB −13 dB
Amplitude uncertainty 0.10 dB 1.42 dB 3.92 dB
Shape factor (60 dB BW/3 dB BW) 2.6 9.1 >300
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