Stanford Research Systems SR780, Operating Manual And Programming Reference

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Display Setup Menu 4-23
SR780 Network Signal Analyzer
Vector Averaging On
Auto Correlation = invFFT( VecAvg( FFTu N ) • conj( VecAvg( FFT N ) ) )
where N is Channel 1 or 2. FFT is a windowed FFT and FFTu is an un-windowed FFT
(uniform window).
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 display which is measuring a single channel correlation
will have its start frequency set to 0 Hz. A display which measures cross correlation will
set the start frequency of both displays to 0 Hz.
A window is applied to the time record of the first FFT 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’ errors where data 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).
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 measuring time delays between two common signals.
The definition of Cross Correlation depends upon the Average Mode selected in the
[Average] menu.
Averaging Off
Cross Correlation = invFFT( FFTu2 • conj( FFT1 ) )
Peak Hold or RMS Averaging On
Cross Correlation = invFFT( VecAvg( FFTu2 • conj( FFT1 ) ) )
Vector Averaging On
Cross Correlation = invFFT( VecAvg( FFTu2 ) • conj( VecAvg( FFT1 ) ) )
where FFT1 is the windowed FFT of Channel 1 and FFTu2 is the un-windowed FFT
(uniform window) of Channel 2.
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 display which is measuring a single channel correlation
will have its start frequency set to 0 Hz. A display which measures cross correlation will
set the start frequency of both displays to 0 Hz.
A correlation window is applied to the time record of the first FFT 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’ errors where data starts to repeat itself. To avoid this,