Separation between average and fluctuation parts in state density in many-particle quantum systems with k-body interactions, modelled by the k-body embedded Gaussian orthogonal random matrices (EGOE(k)), is demonstrated using the method of normal mode decomposition of the spectra and verified using power spectrum analysis, for both fermions and bosons. The smoothed state density is represented by the q-normal distribution (fqN) (with corrections) which is the weight function for q-Hermite polynomials. As the rank of interaction kincreases, the fluctuations set in with smaller order of corrections in the smooth state density. They are found to be of GOE type, for all k values, for both fermion and boson systems.