Phase-increment sampling in chirp signal based impedance measurements

For measuring of the spectra of complex electrical impedance, the chirp excitation signals can be used. The analysis of the response signal of an object, often dynamical, in time, or circuit under test can be performed by short-time Fourier transform in the sliding time-domain window. Computationally more efficient and accurate could be the usage of the simple correlation (multiplication-and accumulation of the discrete samples in the digital processing case) by the excitation waveform (sine chirp) as the first reference signal in the first (“in-phase”) channel and by corresponding cosine-chirp in the other (“quadrature”) channel, both in the same sliding in time window. Still, classical uniform sampling scheme in such solutions is not efficient and not giving accurate result, so the non-uniform sampling scheme of excitation signal and reference waveforms has been proposed and investigated, on some practical examples. For linear chirp - the key is usage of the constant phase increments of the sampling instants of the excitation signal, corresponding to the non-uniform time and frequency increments. Simulations for measurement of the impedance spectra in the frequency range of 10kHz to 1 MHz with 1 ms duration chirp signal has been performed, showing the good performance of the proposed approach at possible simplicity of the implementation.