BSA Flow Software Installation and User's Guide - CSI

Resampling
Sample-Hold
Even with very high data rate the upper frequency of the calculated spectrum
is limited, since the measured velocities are averaged over the time it takes
for the seeding particle to cross the measuring volume, and the transit time
thus limits the upper frequency. For most LDA experiments the latter is no
problem, since normally this upper limit is well above the highest frequency
of interest.
To reduce calculation time, the Fourier transformations in (7-67) are
implemented using Fast Fourier Transformation (FFT). These algorithms
require the discrete samples to be evenly distributed in time, and the process
of converting the discrete representation of the time history record into an
evenly spaced time history record with constant interarrival times is called
resampling.
Several methods for resampling have been suggested, and [Schmidt (1997)]
recommends the use of either sample/hold interpolation or exponential
interpolation by [Høst Madsen & Caspersen (1995)]. Sample/hold
interpolation is the most wide-spread of the two, and also the easiest to
implement:
{ uresamp() t u( ti)| ( tit ti)
}
= ≤ < +1 (7-71)
As shown in Figure 7-83, the sampled velocity is simply assumed to be
constant until a new sample indicates that the velocity has changed.
U(t)
True velocity
Sample/Hold velocity
ti - ti-1 =
Random time
between true
samples
True sample (burst)
Resample
∆t =
Fixed time
between
resamples
Figure 7-83 Random sampling, sample/hold and resampling.
The sampled and held signal is resampled at regular intervals to provide a
series of evenly distributed velocity samples.
This simple approach presents two immediate problems both shown in
Figure 7-83. If two neighboring true samples are further apart than the time
between resamples, the first one will be resampled several times although no
new information about the flow is available. If on the other hand there is
more than one true sample in the time between two resamples, the
information contained in all but the last one will be lost, since the resampling
always take the value of the latest true sample.
7-126 BSA Flow Software: Reference guide
t