Parametric estimation of a biased harmonic signal is a significant technical challenge for many engineering applications. Such a problem is particularly important for electric utility grid-connected power electronic converters. This paper utilizes a linear regression model of the signal to solve this interesting practical problem. A continuoustime dynamic regressor extension and mixing (DREM) based approach is then applied for parameter estimation. For practical implementation, continuous-time estimators are discretized using implicit and explicit Euler methods. We then prove that the implicit discretization can achieve fixed-time convergence for the unknown frequencies estimation. Thanks to the estimated frequencies, another DREM-based linear regression problem is solved for the parameter estimation purpose. The overall order of the proposed technique is the same as the number of unknown parameters, making the estimator suitable for real-time implementation in embedded devices. Theoretical results are validated through extensive comparative experimental studies.