Multiple Frequencies Determination of Sinusoidal Real Waveform by Multiple Sensors With Low Sampling Rate

Sub-Nyquist sampling can be done based on real or complex waveforms for frequency determination. In sensor networks, sampling from real waveform is preferred to the complex one due to hardware resource limitation. Nevertheless, extending the determination procedure of a single frequency to multiple frequencies of real waveform is not straightforward and needs more investigations. In this paper, a mathematical step-by-step procedure of multiple frequencies determination from its under-sampled real waveform is proposed. The maximum frequency and the maximum tolerable noise at which the multiple frequencies can be obtained uniquely from their under-sampled real waveforms are obtained, too. Finally, the performance of the proposed procedure is verified by some simulation results.