A unified formulation of a direct identification method for linear mechanical systems is proposed. Linear operators are applied to the set of motion differential equations, transforming it into an algebraic system. The cases of expansion on Chebyshev polynomials and of Cauchy continuous wavelet transform are studied with a focus on their similarities and differences in writing and performances. Both methods are illustrated and compared by applying them on numerical simulations of two different 3 degrees of freedom systems with non-proportional damping. The effect of additive white noise on signals is also investigated.