This paper validates the use of a harmonic analysis algorithm on a microcontroller to perform measurements of non-stationary signals in the context of smart grids. The increasing presence of electronic devices such as inverters of distributed generators (DG), power converters of charging stations for electric vehicles, etc. can drain non-stationary currents during their operation. A classical fast Fourier transform (FFT) algorithm may not have sufficient spectral resolution for the evaluation of harmonics and inter-harmonics. Thus, in this paper, the implementation of a chirp-Z transform (CZT) algorithm is suggested, which has a spectral resolution independent from the observation window. The CZT is implemented on a low-cost commercial microcontroller, and the absolute error is evaluated with respect to the same algorithm implemented in the LabVIEW environment. The results of the tests show that the CZT implementation on a low-cost microcontroller allows for accurate measurement results, demonstrating the feasibility of reliable harmonic analysis measurements even in non-stationary conditions on smart grids.