We would like to use the VSA software to measure the cross correlations between some signals and found something really strange when using the cross correlation trace : in the following exemple, we are using 2 baseband inputs on the same MXA, but we had the same problem when grouping 2 MXA in one measurement.

On screenshot 1, I am sending a sine at the center frequency on channel 1 and a sine slightly detuned on ch2 (as you can see on the main Time traces on the left). As expected, the Cross Correlation time trace is oscillating at the difference frequency over time, as seen on the lower right channel.

Now, I simply invert the 2 cables going to channel 1 and channel 2, such that channel 2 is excited at the center frequency and channel 1 is slightly detuned. While everything is consistent on the other panels, the lower right one shows a signal that looks completely different from the previous one: the Cross correlation trace is now a flat line that oscillates up and down from trace to trace with an amplitude of plus/minus one square (same as the amlpitude of the sine in the previous test). I don't understand at all this behaviour: I would have expected the cross correlation vector to rotate in the phase space with exactly the same rotation speed, but opposite direction.

What is going on there ? I saw on that thread that the cross correlation signal was not completely symmetric with respect to the 2 time traces involved due to a square filtering window. But I don't see how multiplication by a squared window that's only twice as small as the original timetrace could produce such an effect. It looks like demodulation is not done with respect to the same frequency in both cases or something like that. I keep turning things in my head, but I don't see what is exactly going on there?

I hope the problem is explained clearly enough and someone can help.

Thanks in advance,

Samuel

On screenshot 1, I am sending a sine at the center frequency on channel 1 and a sine slightly detuned on ch2 (as you can see on the main Time traces on the left). As expected, the Cross Correlation time trace is oscillating at the difference frequency over time, as seen on the lower right channel.

Now, I simply invert the 2 cables going to channel 1 and channel 2, such that channel 2 is excited at the center frequency and channel 1 is slightly detuned. While everything is consistent on the other panels, the lower right one shows a signal that looks completely different from the previous one: the Cross correlation trace is now a flat line that oscillates up and down from trace to trace with an amplitude of plus/minus one square (same as the amlpitude of the sine in the previous test). I don't understand at all this behaviour: I would have expected the cross correlation vector to rotate in the phase space with exactly the same rotation speed, but opposite direction.

What is going on there ? I saw on that thread that the cross correlation signal was not completely symmetric with respect to the 2 time traces involved due to a square filtering window. But I don't see how multiplication by a squared window that's only twice as small as the original timetrace could produce such an effect. It looks like demodulation is not done with respect to the same frequency in both cases or something like that. I keep turning things in my head, but I don't see what is exactly going on there?

I hope the problem is explained clearly enough and someone can help.

Thanks in advance,

Samuel

The 89600 cross correlation is computed using the first half of Ch1 Main Time, and the entire Ch2 Main Time. This asymmetry means that the user will see different behavior depending on which channel is exactly at the center frequency, and which is offset.

First, consider the case of Ch1 being exactly at the center frequency. Ch1 Main Time is then a constant value, while Ch2 Main Time is a complex exponential. The cross correlation slides half of Ch1 Main Time (the constant value) along Ch2 Main Time, and computes the dot product at each point. The dot product will have a small magnitude, and could even be zero if there is an integer number of cycles of the offset frequency contained in half the time length. But the phase of the dot product will vary because each dot product starts at a different point in the Ch2 complex exponential. Constant amplitude and varying phase means that the real part of the cross correlation will be sinusoidal.

Then consider the case of Ch2 being exactly at the center frequency. Ch1 Main Time is a complex exponential, while Ch2 Main Time is a constant value. The cross correlation slides half of Ch1 Main Time (the complex exponential) along Ch2 Main Time, and computes the dot product at each point. Since the same first half of Ch1 Main Time is used for every dot product, and Ch2 Main Time is a constant value, each dot product will produce the same value. The value will have a small magnitude (similar to the case above) and a phase that depends on the phase of the complex exponential in Ch1 Main Time.

In order to get the results you expect, you would need to set the analyzer center frequency to the frequency of the signal that is connected to Ch1. This was true in the first case above, but not the second case.

Note that if we had infinitely long signals, the cross correlation between two sinewaves of different frequency would be zero everywhere. But we have only a finite time record, so the computed cross correlation will be non-zero because there won’t necessarily be an integer number of cycles of the sinewave in the time record.