  Random Matrix Theory (RMT) is capable of making predictions for the spectral
fluctuations of a physical system only after removing the influence of the
level density by unfolding the spectra. When the level density is known,
unfolding is done by using the integrated level density to transform the
eigenvalues into dimensionless variables with unit mean spacing. When it is not
known, as in most practical cases, one usually approximates the level staircase
function by a polynomial. We here study the effect of unfolding procedure on
the spectral fluctuation of two systems for which the level density is known
asymptotically. The first is a time-reversal-invariant chaotic system, which is
modeled in RMT by a Gaussian Orthogonal Ensemble (GOE). The second is the case
of chaotic systems in which m quantum numbers remain almost undistorted in the
early stage of the stochastic transition. The Hamiltonian of a system may be
represented by a block diagonal matrix with m blocks of the same size, in which
each block is a GOE. Unfolding is done once by using the asymptotic level
densities for the eigenvalues of the m blocks and once by representing the
integrated level density in terms of polynomials of different orders. We find
that the spacing distribution of the eigenvalues shows a little sensitivity to
the unfolding method. On the other hand, the variance of level number
{\Sigma}2(L)is sensitive to the choice of the unfolding function. Unfolding
that utilizes low order polynomials enhances {\Sigma}2(L) relative to the
theoretical value, while the use of high order polynomial reduces it. The
optimal value of the order of the unfolding polynomial depends on the dimension
of the corresponding ensemble.
