Cross Correlation Homework: Measuring Delay

[EvLer]

Homework Statement

A signal x(t) is transmitted and received back as y(t) and sampled in the receiver, so we get a DT signal
y[n] = ax[n-D] + w[n], where w[n] is noise

baiscally i need to explain how we can measure the time delay by computing crosscorrelation Ryx(l).

My undestanding is:
cross-correlation measures how similar the signals are, so if we ccompute cross correlation of a signal with its reflected version, we will get shifted peaks, and the amount of shifting is the delay


Is this correct?

 

[sravanign]

Can you please solve it?

 

[Evo8]

I realize this is a super old thread. But I was about to ask the exact same question. So I figure I would try bumping it up.

My understanding is very similar to EvLer's. I have a transmitted pulse x(t) and the received pulse is x(t). These are received by a receive and processed to determine the time delay. The distance from the reflecting object is the time delay.

Can anyone provide a little more information to make things clearer or confirm what is above in post or Evler's?

Thanks in advance!

 

[I like Serena]

Hey Evo8!

I can confirm what is in Evler's post.

The cross correlation of x and y has a peak at position D.
Cross correlation can typically be computed with a transform (DFT or other).