0

I'm looking for the method to calculate theoretical similarity of two random noises $x$ and $y$ with mean $0$ and standard deviation $1$, I've got also $12500$ samples of signal, sampled $2.5$ Ga/s.

Due to my idea I wanted calculate the probability that the two noises have coherence $$C_{xy}(f)=\frac{|G(f)_{xy}|^2}{G(f)_{xx}G(f)_{yy}}$$ higher than $0.5$ in frequency range $2$-$20\mathrm{MHz}$? I wanted to compare it with experimental result. I found probably the answer to my question: Statistical significance of coherence values. How to do this for my signal? How $\alpha$ coefficient in this link was calculated?

Malum Wolfram
  • 1
  • 1
  • What is $G(f)_{xy}$? Also, your question is only borderline signal processing-related -- can you give more context of your application? – MBaz Jun 12 '20 at 00:38
  • @MBaz $G(f){xy}$ is cross-spectral density, here is definition: link[https://en.m.wikipedia.org/wiki/Coherence(signal_processing)] – Malum Wolfram Jun 12 '20 at 01:47
  • @Malum Wolfram: Hi. I may not be understanding but your question seems paradoxical because, if both signals are truly white noise ( well, white noise is imaginary but theoretically speaking ), then, by definition, one cannot be predicted from the other. So, assuming that the coherence is the frequency analogue of cross-correlation, it should be close to zero and not statistically significant. This is because of the definition of white noise. – mark leeds Jun 12 '20 at 11:38
  • @markleeds Can we really not have two random white noise signals that are not correlated to each other? Consider the input and output of an amplifier that is amplifying a white noise signal. (Also confusing use of imaginary---which is why I dislike that we decided to call j or i that). – Dan Boschen Jun 12 '20 at 12:56
  • @MalumWolfram See my answer here for computing the correlation coefficient: https://dsp.stackexchange.com/questions/30847/noise-detection – Dan Boschen Jun 12 '20 at 12:58
  • 1
    @Dan Boschen: I know zero about amplifiers ( and not much about DSP either ) but, if two different RV's are truly white noise, then, by definition, they can't be correlated. Part of their definition is that they are uncorrelated. – mark leeds Jun 12 '20 at 16:30
  • @markleeds we can have A= 5B where B is one signal and A is another. B is truly white noise. A is too. A and B are correlated. This is an extreme case where they are basically the same signal but we would capture signals at different points in a receiver chain (such as the amplifier example, or between what is transmitted and what is actually received and treat these as two separate signals with an interest in correlated to see if they are in fact the same signal or not. Each one on its own can have all the properties of being white noise. – Dan Boschen Jun 12 '20 at 17:37
  • gotcha. I was talking about the case where there are two totally different RV's. In your case, the signals are perfectly correlated, but, in statistics, your example would be considered the same random variable. So, the confusion due to a difference between statistics and DSP. – mark leeds Jun 13 '20 at 17:43

0 Answers0