Waveform synthesis of multi-frequency sinusoids with 2nth primary harmonics based on Walsh functions

Excitation source with multi-frequency sinusoids is of importance for bioimpedance spectroscopy (BIS) measurements. This paper describes a novel and simple method to synthesize multi-frequency sinusoids with 2ⁿth primary harmonics based on Walsh functions. The synthesis mechanism is presented detailedly, and after analyzing the Fourier series expression of the periodic signal, the expression of the synthesized waveform in time domain is obtained. The simulation amplitude spectra and power spectra results confirm that the energy of the synthesized signal is concentrated on the expected 2ⁿth primary harmonics, and the bandwidth of the signal is also controllable, which foretell that the proposed waveform synthesis will be an ideal excitation source for spectral measurements. Furthermore, as a binary valued function, the waveform can be generated by FPGAs easily and has a great value in BIS measurements.