On a property of Wiener filters

Let
Y(\omega,\alpha)
be the Wiener filter designed to yield an output which is the least-square approximation to
s(t + \alpha)
where
s(t)
is the desired signal input. Let
Y_L(\omega)
be the Wiener filter designed to yield an output which is the least-square approximation to some linear operation
L
on the desired input signal. The following simple relationship has been shown to hold between
Y(\omega, \alpha)
and
Y_L(\omega)
. If
s(t)
is the desired input signal and
L_{\alpha}[s(t + \alpha)
is the desired output, where
L_{\alpha}
is some linear operation with respect to
\alpha
, then
Y_L(\omega) = L_{\alpha}[Y(\omega, \alpha)]
.