1) Let us say, I have 2x2 matrices A and B. I have another matrix C which is 4x4 , that is , C=[A X ; XT B]. Where X is the 2x2 covariance matrix between A and B. How can I calculate Correlation Coefficient?
The formula of Correlation Coefficient for two random variables X and Y is Corr=Cov(X,Y)/Std(X)*Std(Y). How can I calculate Correlation coefficient in above case?
2) If I have a Matrix A=[2 0;0 9]; If I rotate this matrix between 0 to 360, I get a maximum correlation of -0.6365 to 0.6365. How can I achieve maximum correlation of 1 or 0.9 for this matrix using rotation?
Kindly help me out. Any suggestions and comments?
Mathematically a cross-correlation is only defined between two matrices or images of equal size. If you have images of different size but same aspect ratio then you can re-size the larger by down-sampling onto the same size as the smaller using various integration and/or interpolation schemes or up-sampling the smaller image to the bigger size by pixel repeat.
In your above example, it's not clear which matrices you want to do the cross-correlation between. If it's A and B then it's straightforward. If it's A and C then I suggest you upsample A to a 4x4 matrix of [ 2 2 0 0; 2 2 0 0; 0 0 9 9; 0 0 9 9].
If it is in Matlab than you can use
The sample given is done based on LScode2
code=LScode2(11);
for i=0:7
for j=-8189:8190
cc(i+1,j+8190)=sum(code(1,:).*circshift(code(i+1,:)',j)');
end
end
close all;
subplot(111);
for i=1:8
subplot(4,2,1);
stem(cc(i,:),'.');
title(['Cross correlation of code ',num2str(1),'and code ',num2str( i)]);
end
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