Time-Lag of Harmonic Signals

[CaptainBobble]

Hi,

I'm hoping somebody will be able to help with a problem I'm having calculating the time lag between two signals, one of which is at a subharmonic frequency of the other.

This is a synchronisation case: one signal is a driving signal at frequency f, and the other signal is "locking-on" to the subharmonic f/2. I want to calculate the phase/time lag between the signals but I am unsure of the validity of standard cross-correlation techniques in these circumstances.

I have been using Matlab's "xcorr" function, and I tried it with dummy harmonic signals and a given lag but the results were not promising.

Thanks in advance for your help. My background is fluid dynamics, not pure maths so please keep answers simple for me!

 

[VEBill]

In the real world, one would simply examine the zero crossing points on an oscilloscope. This would reveal the time lag directly, assuming that the time lag wasn't so large that it had wrapped around.

 

[2dye4]

I take it you know the shape of the signals which would be necessary to find them in the cross correlation.

Your approach should work reasonably well by xcorr the overall signal with each of the known subsignals and compare the time difference in the xcorr results for each one.

Of course your results may vary if the source is very noise and the known signals are relatively small.

In this case you may xcorr with an extended function that contains multiple copies of the target signal strung together.

Good luck

 

[VEBill]

The problem description seemed to imply that the two signals are more-or-less sinusoidal (as opposed to complex waveforms).

 

[CaptainBobble]

Hi VE1BLL,

Thanyou for your response to the question. Yes, the driving signal is a pure sinusoid and the entrained signal is a more noisy sinusoid. The actual physical case is a wing in a wind tunnel that is being driven in pitch but left free to roll.

We are interested in finding by how much the roll response lags the pitch motion.

I have tried to research the validity of cross-spectral analysis techniques under conditions of differing frequencies but haven't been able to get a clear answer.

Luke

 

[VEBill]

Not my area of knowledge, but you might want to consider if the position of pitch leads to a roll force (that eventually changes the roll position). In other words, the positions (that you're probably measuring) might not be directly related.

For a given set of circumstances, you should be able to examine the two waveforms (almost by eye), and measure the time lag based on reference points such as a zero crossing point. At the very least, this would be a good sanity check to make sure that other methods give you the correct answer.

The subharmonic needs to be explained too. It's not clear where the divide-by-two would be originating, unless it's only occuring a relatively high frequencies.

 

[IRstuff]

If you do a full-blown FFT, wouldn't you get the phase of the two frequencies?


As for the subharmonic, wouldn't that indicate that it is a resonant frequency being driven by external excitation. I vaguely recall a rule of thumb that says that you need to be half a decade away from the resonance ensure no excitation of the resonance.

TTFN

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[CaptainBobble]

My understanding is that this is a case of synchronisation (see

http://www.scholarpedia.org/article/Synchronization)

which I guess is similar to resonance. The driven signal gets attracted and locks-in to the drive frequency when the drive frequency is close to the natural frequency or harmonics thereof.

Luke

 

[2dye4]

I think Irstuff is correct. Capture the combined signal and then run the FFT on it.

the result will be a complex array of points the same length as the original.

get the complex values for the two frequencies.

Use

angle(z)

Which returns the degrees in radians for the frequency component.

convert the phases to time for each point using its unique frequency.