corrcoef & xcorr
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Hello i've two complex functions ( size 1x1x2501) and i need to do a correlation between these (cross-correlation).
i've tried to use this command:
r=corrcoef(Hmimo_tb(1,:)',Hmimo_tb1(1,:)','coeff');
where Hmimo_tb and Hmimo_tb1 are my two signals in which the only difference is the fact that they have been measured in different positions. The difference betweeen these two signals is max equal to 1.5e-13, so they are only affected by noise.
i obtain as result:
ans =
1.0000 1.0000 + 0.0000i 1.0000 - 0.0000i 1.0000
the function that i'm going to correlate are complex but the 0.0000i leave me some doubts.... Another doubt is the fact that the the signals are not equal in fact as i've told before there is a difference of 1.5e-13 that is not reported on the secondary diagonal why?
what are the difference between corrcoef and xcorr?
采纳的回答
Wayne King
2011-11-10
Salvatore, corrcoef() is not the cross correlation sequence. It does not shift one vector with respect to the other.
x = cos(pi/4*n);
y = cos(pi/4*n-(3*pi)/4);
[r,p] = corrcoef(x,y);
But
[c,lags] = xcorr(y,x,'coeff');
[maxcorr,I] = max(c);
lags(I)
You see that if you allow for shifts then y and x are perfectly correlated and that happens at lag 3, which makes perfect sense since the frequency of x and y is pi/4 radians/sample and y is shifted (3*pi)/4 radians.
Now, note for
lags(length(x))
c(length(x))
This is exactly equal to r in [r,p] = corrcoef(x,y);
7 个评论
Salvatore Turino
2011-11-10
Wayne King
2011-11-10
Salvatore, corrcoef() is the same as xcorr() at lag =0. When one signal is not shifted with respect to the other. xcorr() shifts the signal and then correlates. In the example I gave you, the signals are perfectly correlated if you shift one by three samples. That's what the 3 tells you.
corrcoef() only tells you what the correlation is if you take the vectors as they are WITHOUT shifting one of them with respect to the other.
Salvatore Turino
2011-11-10
Wayne King
2011-11-10
There is nothing wrong per se. It depends on your application. xcorr() tells you the delay between two signals. That can be very important information. corrcoef() does not tell you that.
Salvatore Turino
2011-11-10
Wayne King
2011-11-10
It can mean a phase shift. It depends on the nature of the signals whether it is more natural to view it as a phase shift or just a delay. If the signals are sine waves, I think it is more natural to think of it as a phase shift. Have you tried to understand my examples??? I've shown you a number of example where you find the delay in by the peak in the cross correlation.
Salvatore Turino
2011-11-10
更多回答（2 个）
Walter Roberson
2011-11-10
1 个投票
0.0000i implies that there is a non-zero complex component which is too small to be represented using your current display format (which is probably "format short f")
6 个评论
Salvatore Turino
2011-11-10
Walter Roberson
2011-11-10
format long g
Salvatore Turino
2011-11-10
Salvatore Turino
2011-11-10
Walter Roberson
2011-11-10
With values that small, it could indicate round-off error.
Salvatore Turino
2011-11-10
Salvatore Turino
2011-11-11
1 个评论
Wayne King
2011-11-11
Salvatore, you keep making this mistake. c(3) is not at lag three. You are forgetting about the negative lags. If you enter lags(3) for the example you have above, you see that c(3) is the value of the cross correlation sequence at lag -98. c(104) is the cross correlation sequece at lag 3. That value is very close to 1.
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2011-11-10
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