Dynamic regressor extension and mixing 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, for linear 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 leastsquares estimators. The main result of this paper is to give new techniques for deriving explicit conditions on the exogenously specified reference trajectory to guarantee parameter convergence for a class of linear discrete-time single-input single-output systems. A numerical example is given.