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I have a problem with these two equations showing in the pictures.

Equation 1: Equation 1

Equation 2: Equation 1

1.I have two vectors represented the C(m) and S(m) in the two equations. I am trying to implement these equations in Matlab. Instead of doing a continuous integral operation, I think I should do the summation. For example, the first equation

A1 = sqrt(sum(C.^2));

Am I right? Also, I am not sure how to implement equation two that contains a ||dM||. Please help.

2.What are the mathematical meaning of these two equations? I think the first one may related to the 'sum of squares', if C(m) is a vector then this equation will measure the total variance of the random variable in vector C or some kind of average of vector C? What about the second one?

Thanks very much for your help! A.

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