The main object of the paper is a symmetric system Jy' - B(t)y = lambda DELTA(t)y defined on an interval X = [a, b) with the regular endpoint a. Let phi(^., lambda) be a matrix solution phi(^., lambda) of this system of an arbitrary dimension and let (Vf)(s) = int from I phi^*(t, s)DELTA(t)f(t)dt be the Fourier transform of the function f(^.) є L_DELTA²(I). We define a pseudospectral function of the system as a matrix-valued distribution function sigma(^.) of the dimension n_sigma such that V is a partial isometry from L_DELTA²(I) to L²(sigma; C^n_sigma) with the minimally possible kernel. Moreover, we find the minimally possible value of n_sigma and parameterize all spectral and pseudospectral functions of every possible dimensions n_sigma 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.

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