The paper is devoted to the spectrum of multivariate randomly sampled autoregressive moving-average ({\sl ARMA}) models. We determine precisely the spectrum numerator coefficients of the randomly sampled {\sl ARMA} models. We give results when the non-zero poles of the initial {\sl ARMA} model are simple. We first prove the results when the probability generating function of the random sampling law is injective, then we precise the results when it is not injective.