Stanford Research Systems SR785, Operating Manual And Programming Reference

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2-38 Correlation
SR785 Dynamic Signal Analyzer
Correlation Analysis
What is Correlation Analysis?
Correlation is a time domain measurement which reveals similarities and periodicities
within a signal (autocorrelation) or between two signals (cross-correlation). Although a
time domain measurement, the SR785 computes correlation measurements by
transforming input data into the frequency domain, processing it, and retransforming
back to the time domain.
Correlation Measurements
Correlation Analysis is a Measurement Group. Choose the Measurement Group within
the [Display Setup] menu. The available measurements are Auto Correlation, Cross
Correlation, Time Record, Windowed Time record, Capture Buffer and User Function.
Auto Correlation
Auto correlation is a single channel measurement. In the time domain, it is a comparison
of the signal x(t) with a time shifted version of itself x(t-
τ
) displayed as a function of
τ
.
This is useful for detecting similarities which occur at different times. For example,
echoes show up as peaks separated by the echo time. Sine waves appear as sine waves in
auto correlation and square waves appear as triangles. Signals which do not repeat or are
completely random (such as noise) appear only at
τ
= 0.
The definition of Auto Correlation depends upon the what type of averaging is selected
in the [Average] menu.
Averaging
Auto Correlation = invFFT( FFTuN • FFTN* )
RMS or Peak Hold Averaging
Auto Correlation = invFFT( <FFTuN • FFTN*> )
Vector Averaging On
Auto Correlation = invFFT( <FFTuN> • <FFTN*> )
where N is Channel 1 or 2. FFT is a windowed FFT, FFTu is an un-windowed FFT
(uniform window) 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 display which is measuring a single channel correlation
will have its start frequency set to 0 Hz.
A correlation window is applied to the time record of one 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’ 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