Time-Lag of Harmonic Signals
Time-Lag of Harmonic Signals
(OP)
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!
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!





RE: Time-Lag of Harmonic Signals
RE: Time-Lag of Harmonic Signals
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
RE: Time-Lag of Harmonic Signals
RE: Time-Lag of Harmonic Signals
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
RE: Time-Lag of Harmonic Signals
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.
RE: Time-Lag of Harmonic Signals
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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RE: Time-Lag of Harmonic Signals
Luke
RE: Time-Lag of Harmonic Signals
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.