part of Course 137 Signal Processing Techniques
It's often useful to take a signal and shift and scale it so that it has a particlar mean and variance. For a mean of 0 and a variance of 1, this is known as standardization or Z-score normalization.
During the process, we end up working with
the square root of the variance,
the standard deviation.
For a signal, s having a mean of
μ_s and a standard deviation of σ_s,
you can transform it to a
signal z having
a mean of 0 and a standard deviation of 1 with
z = (s - μ_s) / (σ_s + ε),
where ε is a small number, say 10^-6 or 10^-10, that prevents divide-by-zero errors in the rare cases where &sigma_s; is zero.
That in turn can be transformed to a signal t
having any μ_t and σ_t with
t = z * σ_t + μ_t