BSA Flow Software Installation and User's Guide - CSI

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Power spectrum decays with
f -2 above cut-off frequency
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Frequency [Hz]
n& 2π≅15 . kHz n& ≅ 92 . kHz
Approaching max frequency the estimated
power spectrum flattens due to aliasing
Figure 6-52 The 'Sample-and-hold' technique act as a low-pass-filter attenuating the spectrum.
If you are investigating turbulence this presents a pitfall, since the decay of
spectral power with f -2 can easily be confused with the inertial subrange,
which according to the Kolmogorov spectrum law decays with f -5/3 .
In this case you must carefully check your datarate to verify that the spectral
decay found does indeed represent the physics of your flow, rather than
particle rate filtering of the true velocities.
Investigating peaks in the power spectrum is not affected quite as much by
the particle rate filter: Although the peak value will be reduced above the
cut-off frequency, so will spectral values at neighbouring frequencies, and
the peak itself is still easily recognised as seen in Figure 6-52, showing a
peak at about 2.3 kHz. Above all, the frequency at which the peak occurs is
not affected by the particle rate filter at all.
The problem of particle rate filtering stems from the fact that LDA as such
yield random velocity-samples instead of a continuous signal, and
consequently the problem cannot be avoided. With a sufficiently high
datarate the problem will however be small, and you should thus always aim
at the highest possible datarate in your experiment.
Aliasing Finally the effect of aliasing can be seen clearly in Figure 6-52: Energy
contained at frequencies above the maximum frequency is aliased into the
range investigated, causing the estimated spectrum to flatten out as it
approaches the maximum frequency selected. In this particular example only
very little energy was present above the maximum frequency, and below
approximately 20 kHz aliasing can thus be ignored completely.
Noise floor The effect of aliasing described above can easily be confused with the noise
floor of your measurement, but the true noise floor will itself be damped by
the particle rate filter, and consequently may not be recognised at all.
A suspected noise floor must thus be verified by checking the datarate.
6-54 BSA Flow Software: Options and Add-ons
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