# Cross correlation peak value

I would like to measure the time delay between two signals. By applying the cross correlation I get the time delay or number of samples by the location of the cross correlation peak, however I am interested to know what peak value itself identifies ? I get a large value for the cross correlation peak.

Thank you!

## 2 Answers

It's the correlation coefficient that you get for maximum matching, which is the squared Euclidean 2 norm of the signal $s(t)$, ie. $||s||_2^2$; when you note down the crosscorrelation in terms of integrals, you'll quickly notice that, if you use both signals for correlation, the value for $\tau=0$ is the same as the energy in the signal.

i dont know if understand well your question,forgive me if I answer something you already knwo... The correlation practically between two binary sequences is the number of "agreements"-number of "disagreements",i a few worlds the number of bits that are matching and those not. so when after shifting and shifting and shifting and shifting...you get to the point geting the correlation peak means that there are not any disagreements (mismatching bits) but only agreements (matching bits),hence the two sequences (the one kept steady and the other shifted) are identical (full correlation) . That is a qualitative explanation i found on a textbook,(I can try to dig in and find the title if you are interested) that help me understand the basics...

• I liked your explanation very much.. specially the mismatching and matching part .. I needed to know what exactly cross correlation peak shows – user3506463 Jan 19 '15 at 9:51
• the book i have used explains exactly the correlation process (amazon.co.uk/… correlation peak will be in exactly the same magnitude as your number of samples (give the fact that you have agreements - disagreements,and the number of disagreements is zero while the two sequences are exactly the same and have reached correlation,meaning that are at the point they match exactly)and by number of samples i mean the length of your vector. – Rizias Jan 19 '15 at 10:29
• just make an experiment yourself,by using 1 very small vector,copy it self under on a paper and start rotating and keep track that agreements-disagreement on the side,which is actually the correlation output and that you are going to see plotted.When after shifting enough to get to the point that the two of them are exactly the same you will observe the peak.And you will have unlocked the corellation.Cross-corellation and autocorrelation are the same processes with the difference that in the first we dont know the shifting sequence before hand and in the second we do... – Rizias Jan 19 '15 at 10:38