#### 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`