  We present two linear relations between an arbitrary (real tempered second
order) generalized stochastic process over $\mathbb{R}^{d}$ and White Noise
processes over $\mathbb{R}^{d}$. The first is that any generalized stochastic
process can be obtained as a linear transformation of a White Noise. The second
indicates that, under dimensional compatibility conditions, a generalized
stochastic process can be linearly transformed into a White Noise. The
arguments rely on the regularity theorem for tempered distributions, which is
used 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. The first linear relation obtained allows also to conclude that any
generalized stochastic process has an orthogonal representation as a series
expansion of deterministic tempered distributions weighted by uncorrelated
random variables with summable variances. This representation is then used to
conclude the second linear relation.
