corrcoef & xcorr

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?

Answer 1

[Wayne King]

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);

[Salvatore Turino]

wait i'ven't understood well.... let's analyze step by step:

x = cos(pi/4*n);

y = cos(pi/4*n-(3*pi)/4);

[r,p] = corrcoef(x,y);

i've created a n=0:1:100 and i obtain as result:

r =

1.0000 -0.7108

-0.7108 1.0000

p =

1.0000 0.0000

0.0000 1.0000

Instead:

[c,lags] = xcorr(y,x,'coeff');

[maxcorr,I] = max(c);

lags(I)

gives me as result 3, what does this mean?

lags(length(x))-->result 0

c(length(x))-->result -0.7106

i'ven't understood the point.

my problem with the correlation of xcorr is that it gives a lot of values in the variable "c" . What i need is a a "single value" , and xcorr gives me a bunch of values. That's because it is calculating the cross-correlation for all the possible array offsets- kind of like a convolution.

the question that i want to ask you is: from this bunch of values how can i be sure that the 2 measure/functions are correlated?for the fact that there is in one of the lags, the one centered in the phase 0, the result 1? if yes all the other lags are negligible?

again thank you for you replies...i know i'm hard to understand ^^

[Wayne King]

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]

ok but explain me why i have to shift the signal?

i have 6 measure syncronized i only want to know if they are correlated and how much they are near to be. in what i wrong if i take only the value at lag=0?

[Wayne King]

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]

ok great!let me understand the last thing for delay you mean a shift of the phase? and if yes how can i recognize it?

[Wayne King]

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]

ok so i understand that the results different from the lag-0 have a non-clear meaning or bytheway what i want to study deeper is if for example the xcorr between M1(measure 1) and M2 gives in the lags=1000 c=0.002 how much shifted is respect the c=0.003 in the lags=1000 of the xcorr between M1 and M3?

Answer 2

[Walter Roberson]

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")

[Salvatore Turino]

how can i change the display format?

[Walter Roberson]

format long g

[Salvatore Turino]

Column 1

1

1 - 3.73593550274545e-11i

Column 2

1 + 3.73593550274545e-11i

1

it works.

[Salvatore Turino]

the fact that on the secondary diagonal i have a complex value means that the two signals have different phase or what?

[Walter Roberson]

With values that small, it could indicate round-off error.

[Salvatore Turino]

mmm well consider that also in the positive value there is a round-off error in my opinion in surplus because the two measurements are not equal (but near to be). does exist a way to not have this approximation?

Answer 3

[Salvatore Turino]

Wayne i've tried your code

x = cos(pi/4*n);
 y = cos(pi/4*n-(3*pi)/4);
 [r,p] = corrcoef(x,y);

[c,lags] = xcorr(y,x,'coeff');
 [maxcorr,I] = max(c);
 lags(I)

but i'm on trouble. i've set n=0:1:100 and as you say i have as result 3. you say that those functions are correlated at lags 3 but watching the "c" if lags 3 correspond to c(:,3) i have this result: -0.0139333076031825

so why do you say that they are perfectly correlated?

[Wayne King]

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.