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I am new to electronic engineering and DSP. I have this orignal signal matrix [X1,Y1] . . . . [Xn,Yn]

and then it goes through series of transformation. It can be rotation/shift_bit/or whatever transformation through a transformation Matrix. so suppose through this operation I will have A1....Am matrix from the original signal

and I have another signal. but go through different transformation not necessarily the same as above. let say B1...Bm

now if I mix the two bags A1...An and B1...Bm together. And then draw from these combine bag randomly of the two matrix How can I determine the two matrix Ai = Bj

I am thinking using spectral analysis but not sure if it is the right path and also if any R/Matlab/python package can help this work ??

-Thx sincerely.

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2 Answers 2

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The statistical test for whether two signals ("samples" in stats language) are equivalent ("are drawn from the same distribution") is a test like t-test (for normal variables), paired sample t-test (if these are two signals measured at the same times), Mann-Whitney U test, Wilcoxon rank-sum test, etc.

There are a few things that make it hard to give specific answer in your case. I think when you say "matrix" you mean vector or perhaps time series. And it is really unclear what you mean by "mix together" (add?) and by "bags". Why mix them? Why draw randomly? Can't you just use a statistical test on the samples without mixing them?

If you can edit the question to show actual formulas or better source code, you could get a better answer.

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Assuming you want to determine the similarity or equivalence of two signals (because your question is not very clear), one of the main methods to achieve this is cross correlation.

Cross correlation takes two signals (or Vectors) as inputs and measures the similarity as one signal is delayed versus the other, one time step at a time.

$$\phi_{xy}(m)=\sum_{n=-\infty}^\infty x(n) y(n+m)$$

So the cross correlation of gaussian white noise signals is an impulse at m=0.

The cross correlation of the noise signal that is phase shifted with respect to the same signal by time 5T is an impulse at m=5

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  • \$\begingroup\$ You are not correct on the last statement. The cross correlation of two signals shifted by 5T would be some function with a peak (maximum) at 5T. It won't be just an impulse. \$\endgroup\$
    – Mike
    Feb 12, 2015 at 10:06
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    \$\begingroup\$ I was referring to the noise signal mentioned in the previous paragraph. Clarified. Thanks. \$\endgroup\$
    – akellyirl
    Feb 12, 2015 at 11:24

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