Precise wide-band electrical impedance spectroscopy measurement via an ADC operated below the Nyquist sampling rate

Abstract Usually, an analog-to-digital converter (ADC) used for electrical impedance measurement is required to operate above the Nyquist sampling rate of excitation signals to ensure the accurate discretization. This paper proposed a robust impedance measurement method in wide-band spectrum via using compressive sensing to eliminate this requirement. The excitation signals were compressed by a random-modulator and a low-pass filter with bandwidth below the excitation frequency, then impedance is recovered by the reconstruction algorithm with the filter parameter identified on-line and the data recorded by the ADC operated just above the Nyquist rate of the filter bandwidth. In the simulations and experiments, a sparse wide-band impedance spectroscopy from 0.01 to 1.05 MHz was sampled by an ADC operated with fixed sampling rate 400 kHz, and the results is comparable to the impedance analyzer. Impedance imaging experiment results demonstrated that the impedance measurement could be precisely achieved for both single- and multi- frequencies.