Digital Frequency Determination of Real Waveforms Based on Multiple Sensors With Low Sampling Rates

Conventionally, a frequency can be uniquely determined when the sampling rate is higher than the Nyquist rate. In some applications, such as sensor network with low transmission rate sensors, it is necessary that the sampling rate to be under the Nyquist rate; in this case, a frequency determination method based on its under-sampled waveform is needed. Several studies have been done to extract real input frequency from under-sampled sinusoidal complex waveform. This paper presents a novel method for unambiguous and unique frequency determination of under-sampled real sinusoidal waveform. The proposed method needs a low cost hardware in compare with the frequency determination of under-sampled sinusoidal complex waveform. First, we determine the upper frequency bound which the frequency can be extracted unambiguously from under-sampled real sinusoidal waveform. Then, in order to extract real input frequency unambiguously and uniquely, the maximum tolerable amount of frequency error is determined from under-sampled sinusoidal real waveform. Moreover, we improve the previous method for frequency determination from under-sampled sinusoidal complex waveform. Finally, performance of the proposed schemes is verified by some simulation results.