  The main object of the paper is a symmetric system $J y'-B(t)y=\l\D(t) y$
defined on an interval $\cI=[a,b) $ with the regular endpoint $a$. Let
$\f(\cd,\l)$ be a matrix solution of this system of an arbitrary dimension and
let $(Vf)(s)=\int\limits_\cI \f^*(t,s)\D(t)f(t)\,dt$ be the Fourier transform
of the function $f(\cd)\in L_\D^2(\cI)$. We define a pseudospectral function of
the system as a matrix-valued distribution function $\s(\cd)$ of the dimension
$n_\s$ such that $V$ is a partial isometry from $L_\D^2(\cI)$ to
$L^2(\s;\bC^{n_\s})$ with the minimally possible kernel. Moreover, we find the
minimally possible value of $n_\s$ and parameterize all spectral and
pseudospectral functions of every possible dimensions $n_\s$ by means of a
Nevanlinna boundary parameter. The obtained results develop the results by Arov
and Dym; A.~Sakhnovich, L.~Sakhnovich and Roitberg; Langer and Textorius.
