Performing reliable calculations of power system dynamics requires accurate models of generating units. To be able to determine the parameters of the models with the required precision, a well-defined testing procedure is used to record various unit transient signals. Unfortunately, the recorded signals usually contain discontinuities, which complicates the removal of the existing harmonic interferences and noise. A set of four transient signals recorded during typical disturbance tests of a 200 MW power-generating unit was used as both training and research material for the signal denoising/interference removal methods compared in the paper. A systematic analysis of the measured transient signals was conducted, leading to the creation of a coherent mathematical model of the signals. Next, a method for denoising power-generating unit transient signals is proposed. The method is based on Sparsity-Assisted Signal Smoothing (SASS) combined with optimization algorithms (simulated annealing and Nelder-Mead simplex) and is called an optimal SASS method. The proposed optimal SASS method is compared to its direct Linear Time-Invariant (LTI) competitors, such as low-pass and notch filters. The LTI methods are based on the same filter types (Butterworth filters) and zero-phase filtering principle as the SASS method. A set of specially generated test signals (based on a developed mathematical model of the signals) is used for the performance evaluation of all presented filtering methods. Finally, it is concluded that—for the considered class of signals—the optimal SASS method might be a valuable noise removal technique.