Built-in MATLAB RMS function

Theoretically, RMS is defined as Rq=sqrt((1/n)*summation(z-zmean)^2))

(courtesy: gwyddion.net) http://gwyddion.net/documentation/user-guide-en/roughness-iso.html

The MATLAB inbuilt function I found in the help section is as follows: MATLAB code for RMS determination y = sqrt(sum(u.*conj(u))/size(u,1))

Questions: 1)Is 'u' defined by matlab the same as 'z-zmean' elsewhere. 2)The term within summation corresponds to the deviations from each data point. Does the matlab inbuilt function correspond to the same? 3) How does the function 'conj(u)' help in determining deviations from a data point?

Please help me out at the earliest with your valuable suggestion as I have a deadline.

Thanks in advance Vinod

Answer 1

[Jan]

The RMS formula of gwyddion concerns the term "z-zmean", while MATLAB's RMS concerns u. If u=z-zmean, both formulas reply the same value.

The difference is, that gwyddion considers real values only, while MATLAB cares for complex values by using CONJ in addition. For real values u==conj(u) and:

u .* conj(u)  ==  u .* u  ==  u .^ 2