Spectral analysis represents a key component in signal processing. The on-chip implementation of classical spectral estimation techniques is generally not considered as a viable BIST solution because of the huge amount of required additional circuitry (multipliers, complex operators). This paper describes a new method for spectral parameter estimation allowing the extraction of the first harmonic with only very simple operators. This method is based on Fourier series expansion and a piecewise algorithm. The results are validated using simulations and experiments, and the method showed relevant results to an embedded solution.