  We use the techniques developed in [1] to study the local average of random
fields with spectral density $1/f^{\alpha}$. We study their scaling properties
and show that the self-similarity of $1/f$ random fields is preserved under the
local average. We study how the original random fields can be recovered from
the locally averaged ones. We also study the derivative of the locally averaged
random fields as a way to get the spectral density. Finally, we propose the
generalization of local average by means of an arbitrary response function.
