Crest factor optimization of the multisine waveform for bioimpedance spectroscopy

The multisine excitation is widely used in impedance measurements to retain the advantages of the sine wave, while reducing the measurement time. Adding up sine waves increases the amplitude of the excitation signal, but, for the linearity assumption to be valid, the overall amplitude of the signal needs to be kept low. Thus, the crest factor (CF) of the excitation signal must be minimized. A novel empirical method for the minimization of the CF is described in this paper. As in the case of other known methods, the computed CF may be guaranteed to be only a local minimum. However, a systematic variation of initial parameters, which is possible due to the sparing algorithm, ensures a CF value very close or equal to the global minimum. The results of CF minimization and comparison with the results from other sources are provided. The direct CF optimization results (set of optimal phases) are not well suited for practical implementation. The influence of phase accuracy on the CF is discussed, and an algorithm for the recalculation of initial phases to the rougher set is described. It is shown that previously obtained optimization results (minimal CF) can be highly preserved, even in the case of rough phase resolutions. The CF of the multisine also depends on the frequency distribution and amplitudes of its components. The CF of multisines with several frequency distributions are compared.