RMS (root mean square) value

RMS value

• measure the size of an n-vector x:
  • $\mathrm{rms}(x):=\sqrt{\frac{1}{n}||x|{|}_2^2}=\frac{1}{\sqrt{n}}||x|{|}_2$
• the de-meaned vector
  • $\tilde{x}=x-avg(x)1=x-\frac{1}{n}(1^{T}x)x$
• the variance: spread of values x around its average
  • $\mathrm{var}(x):=\frac{1}{n}\Vert \tilde{x}{\Vert }_2^2$
• standard deviation std
  • $std(x)=\sqrt{var(x)}=rms(\tilde{x})$