  We show that any (real) generalized stochastic process over $\mathbb{R}^{d}$
can be expressed as a linear transformation of a White Noise process over
$\mathbb{R}^{d}$. The procedure is done by using the regularity theorem for
tempered distributions to obtain a mean-square continuous stochastic process
which is then expressed in a Karhunen-Lo\`eve expansion with respect to a
convenient Hilbert space. This result also allows to conclude that any
generalized stochastic process can be expressed as a series expansion of
deterministic tempered distributions weighted by uncorrelated random variables
with square-summable variances. A result specifying when a generalized
stochastic process can be linearly transformed into a White Noise is also
presented.
