In the paper the application of nonlinear and non-recursive Newton Type Estimation Numerical Algorithm for voltage and current spectra estimation during off-nominal frequency condition and severe signal distortions is presented. The algorithm is not sensitive to power system frequency changes and voltage and current amplitude distortions. It is an important improvement with regard to the commonly utilized approaches based on e.g. Discrete Fourier Transform, or other approaches derived in spectral domain. The unknown frequency is simultaneously measured (estimated) with the spectrum of the input signal. The algorithm is tested using voltages and currents obtained from the ATP-EMTP simulation program, using Simulink model and in laboratory conditions. In the first test, a typical MV network example is used. By this, a motor start and a short circuit followed with the current transformers saturation transients are particularly analyzed. The purpose of Simulink test is to compare the NTA algorithm with FFT. Laboratory test consists of connecting a synchronous generator to the network, when synchronization is not ideal and severe disturbance of generator currents and voltages occur.