Cross Correlation Homework: Measuring Delay

In summary, the conversation discusses how to measure time delay by computing cross correlation of a received signal with its reflected version. The amount of shifting in the cross correlation peak represents the time delay and can be computed using a transform.
  • #1
EvLer
458
0

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?
 
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  • #2
Can you please solve it?
 
  • #3
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!
 
  • #4
Hey Evo8! :smile:

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).
 
  • #5


Yes, your understanding is correct. Cross-correlation is a useful tool in signal processing for measuring the similarity between two signals. In this case, by computing the cross-correlation between the transmitted signal x(t) and the received signal y(t), we can determine the amount of delay (D) between the two signals. This is because the cross-correlation function will have a peak at the delay value, indicating the maximum similarity between the two signals. By finding the location of this peak, we can measure the delay between the transmitted and received signals. It is important to note that noise can affect the accuracy of this measurement, so it is important to account for noise in the computation of the cross-correlation function. Overall, cross-correlation is a useful tool for measuring delay and can be applied in various fields such as telecommunications, radar, and speech recognition.
 

1. What is cross correlation and how is it used in measuring delays?

Cross correlation is a statistical measure that quantifies the similarity between two signals as a function of the displacement of one relative to the other. In the context of measuring delays, cross correlation can be used to determine the time delay between two signals, such as an input and an output signal in a system.

2. What types of signals can be used in cross correlation for measuring delays?

Any type of signal or data can be used in cross correlation for measuring delays, as long as they are time series data. This includes signals from physical systems, such as audio, video, or sensor data, as well as numerical data from simulations or experiments.

3. What are the steps involved in performing cross correlation for measuring delays?

The first step is to collect the two signals that will be used in the cross correlation. Then, the signals are pre-processed to remove any noise or unwanted components. Next, the signals are cross correlated using a mathematical formula, such as the Pearson correlation coefficient or the cross correlation function. Finally, the time delay is calculated based on the peak or maximum value of the cross correlation function.

4. Are there any limitations to using cross correlation for measuring delays?

Yes, there are a few limitations to consider when using cross correlation for measuring delays. One limitation is that cross correlation assumes a linear relationship between the two signals, so it may not be accurate for signals that have a non-linear relationship. Additionally, cross correlation is sensitive to noise and may give inaccurate results if the signals are too noisy.

5. How can cross correlation be used in real-world applications?

Cross correlation has many practical applications, such as in signal processing, communication systems, and time series analysis. It can be used to measure the delay between audio signals in speech recognition systems, to synchronize signals in wireless communication, and to detect patterns in financial data. It is also commonly used in scientific research to analyze experimental data and to study the relationships between different variables.

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