Stanford Research Systems SR785, Руководство по эксплуатации и программированию

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Correlation 2-39
SR785 Dynamic Signal Analyzer
quarter of the time record. The [-T/2..T/2] is a uniform window which should only be
used on data which is self windowing (lasts less than half of the time record).
Cross Correlation
Cross correlation is a two channel measurement. In the time domain, it is a comparison
of a signal x(t) with a time shifted version of another signal y(t-
τ
) displayed as a function
of
τ
. This is useful for detecting signals common to both channels but shifted in time.
The definition of Cross Correlation depends upon the displayed average selected in the
[Average] menu.
No Averaging
Cross Correlation = invFFT( FFTu2 • FFT1* )
Peak Hold or RMS Averaging On
Cross Correlation = invFFT(< FFTu2 • FFT1*> )
Vector Averaging On
Cross Correlation = invFFT( <FFTu2> • <FFT1*> )
where FFT1 is the windowed FFT of Channel 1, FFTu2 is the un-windowed FFT
(uniform window) of Channel 2 and invFFT is an inverse FFT.
Correlation is a real function and requires a baseband span (real time record). Non-
baseband time records do not preserve the original signal frequencies and thus do not
yield the correct correlation.
A correlation window is applied to the time record of Ch1 in the computation. This is
because the FFT models the time domain as a single time record repeating itself over and
over. Computing the correlation over a
τ
greater than half of the time record length will
result in ‘wrap around’ where the correlation starts to repeat itself. To avoid this, special
windows which zero half of the time record are used. The [0..T/2] window zeroes the
second half of the time record and the [-T/4..T/4] window zeroes the first and last quarter
of the time record. The [-T/2..T/2] is a uniform window which should only be used on
data which is self windowing (lasts less than half of the time record).
Time Record
Windowed Time Record
These correlation group measurements are similar to their FFT group counterparts. The
major differences are:
1. Because correlation is a baseband measurement, the time records are never
heterodyned, and are therefore always real.
2. Correlation uses a different set of windows than the FFT measurement group.
The Correlation windows, which are described above, are designed to zero half
of the time record in order to eliminate "wrap-around" error.