Delay estimation using cross correlation

[nauman]

Hi

Suppose there are two continuous signals of same frequency say 4 KHz. The time corresponding to its one cycle is around 250 us. If we delay one signal by 4010 us (i.e >> one cycle delay), can we use cross correlation techniques to estimate this delay accurately?

Thanks

 

[FactChecker]

We need to be careful here. If you said that the delay of a 4 KHz signal was 4000, then there would be no way to distinguish that from a zero delay or from any delay of multiple of 1/4,000 = 250 us.
Since you specified 4010 rather than 4000, that delay could be detected if extreme accuracy was possible. But there are many shorter delays that would be very close to a perfect match. So there is a question of whether the algorithms you use apply a tolerance that would make it appear that a shorter delay is close enough to give for the answer. The presence of any noise would make the calculation much trickier.

 

[nauman]

But there are many shorter delays that would be very close to a perfect match. So there is a question of whether the algorithms you use apply a tolerance that would make it appear that a shorter delay is close enough to give for the answer. The presence of any noise would make the calculation much trickier.

These two signals are from two sensors which are some distance apart and the delays estimated using cross correlation will be utilised for bearing estimation. I am stuck here how to proceed? According to literature, bearing estimation using delay measurements is a standard technique being used.

 

[FactChecker]

These two signals are from two sensors which are some distance apart and the delays estimated using cross correlation will be utilised for bearing estimation. I am stuck here how to proceed? According to literature, bearing estimation using delay measurements is a standard technique being used.

I see. Then you will just have to be very accurate in the calculations and have enough data to minimize the influence of noise.

 

[nauman]

I see. Then you will just have to be very accurate in the calculations and have enough data to minimize the influence of noise.

Yes you are right that noise will have to be catered.
However, what about delays which are greater than one cycle length?
As I have understood so far, cross correlation techniques can measure only those delays accurately which are less than one cycle length in case of single frequency signals. Am i right in my understanding?

 

[FactChecker]

In theory, with unlimited data and accuracy and a sample frequency small enough, the cross-correlation will be greatest at the correct delay. Of course, there is no way to distinguish it if the delay is an exact number of wavelengths since the signals will overlay.