BSA Flow Software Installation and User's Guide - CSI

this approach is referred to as blocking, and the accuracy of the final
autocorrelation function increases with the number of blocks.
The duration Tb of each block equals the desired maximum lag-time τmax,
and consequently the number of blocks Nb can be determined from the total
duration Ttot of the experiment:
Tb = τmax N b ≤ Ttot / τmax
-where Nb is rounded to the nearest lower integer value.
To get as many blocks as possible within the limited duration of the
experiment, short blocks are desirable, but there is a lower limit.
First of all each block must contain a reasonable amount of raw data in order
to get meaningful results: It is thus required that each block contain at least
16 raw samples. Normally the number of blocks included in the calculation
will increase as the maximum lag-time decreases, but since blocks including
less than 16 raw samples are excluded, the total number of blocks will
decrease, when you approach this limit.
Furthermore you must be aware that within each block only very limited
information is available regarding the larger lag-times; -In fact only a single
sample pair (the very first and the very last sample) truly provides
information regarding correlation at the desired maximum lag-time.
Consequently you should always select a maximum time-lag considerably
larger than the highest lag-time of any real interest:
To get reasonable results in turbulent flows the maximum lag-time should
thus be at least 10 times the integral time-scale τI, and preferably even
higher; A maximum time-lag of 50 or even a 100 times τI is not excessive,
provided it does not reduce the number of blocks too much.
Similarly the maximum time-lag should be at least 10 times the period if you
wish to estimate the autocorrelation of a cyclic flow.
Please be aware that the correlation is actually calculated as the inverse
Fourier transform of a spectrum estimate, which in turn has been calculated
using the FFT-techniques described in section 0.
Consequently aliasing may distort correlation-estimates if the flow contains
significant turbulent energy above the resampling frequency; Prior to FFT
the raw data is resampled with a resampling frequency determined from the
desired number of correlation estimates, and the desired maximum lag-time:
f
res
N est 1
= =
τ ∆ τ
max
-where fres is the resampling frequency, Nest is the number of correlation
estimates, τmax is the desired maximum lag-time, and ∆τ is the lag-time
resolution achieved. In other words aliasing may distort the estimated
autocorrelation function if the lag-time resolution is too coarse.
Note: In order to avoid aliasing the maximum lag-time can in principle be reduced
and/or the number of correlation estimates increased to produce arbitrarily
high resampling frequencies. You should be aware however that apart from
an increase in the calculation time a resampling frequency significantly
above the mean datarate of the raw samples has almost no effect on the
correlation estimate as shown in Figure 6-63.
6-66 BSA Flow Software: Options and Add-ons