Cross Correlation Functions: Advanced Applications & Conclusions

[csopi]

Hi.

Can somebody recommend a good book (advanced level) dealing with applications of cross correlation functions? I mean what kind of conclusions can be drawn etc?

 

[jasonRF]

Cross correlation functions are used a lot to estimate coherence and time delay between two timeseries. Under certain assumptions the maximum likelihood estimate of time delay uses the cross-correlation function. This is done all the time in signal and image processing. Carter is a name that comes to mind as someone who has published a lot in this area if you want to look in the literature. Not sure if there are any good books on this, though.

good luck,

jason

 

[Squatchmichae]

I would recommend thinking of cross-correlation as an application of using inner product spaces. If that sounds a little advanced, no worries--it's not as scary as it sounds.

You can think of cross-correlation in terms of probability estimates (coherence and maximum likelihood) or in terms of deterministic problems. Seismology signal processing papers (many online, for free) make good teaching guides. In addition, seach terms for "matched filter". Sometimes an explicit application is great for teaching. If you have access to MATLAB, this also makes for a good teaching tool. You can use xcor to your hearts content. Finally, if you use cross-correlation with it's Fourier Transform Theorem, you will find the properties more useful. It is a great tool! Good luck.