Dynamic regressor extension and mixing (DREM) is a new technique for parameter estimation that has proven instrumental in the solution of several open problems in system identification and adaptive control. A key property of the estimator is that, by generation of scalar regression models, it guarantees monotonicity of each element of the parameter error vector that is a much stronger property than monotonicity of the vector norm, as ensured with classical gradient or least-squares estimators. On the other hand, the overall performance improvement of the estimator is strongly dependent on the suitable choice of certain operators that enter in the design. In this paper, we investigate the impact of these operators on the convergence properties of the estimator in the context of identification of linear single-input single-output time-invariant systems with periodic excitation. The most important contribution is that the DREM (almost surely) converges under the same persistence of excitation (PE) conditions as the gradient estimator while providing improved transient performance. In particular, we give some guidelines how to select the DREM operators to ensure convergence under the same PE conditions as standard identification schemes.