Frequency Uncertainty Resolution with Sub-Nyquist Sampling of Real-value Harmonic Signals

In contrast to the aperiodic spectrum of an analog signal, the spectrum of the sampled signal becomes periodic, and the period is equal to the sampling frequency. With sub-Nyquist sampling, the sampling rate is significantly lower than that required by the sampling theorem. The spectrum then folds to the low frequency region. Therefore, a high frequency harmonic signal can be detected at a substantially lower frequency in the first Nyquist zone. If a harmonic signal is complex-valued, then the true value of the frequency of this signal in a given range is restored using the Chinese remainder theorem. If the signal is real-valued, then the components of the periodic continuation of the mirror image appear in its spectrum, which was at a negative frequency before sampling. As a result, the direct application of the Chinese remainder theorem becomes impossible. This paper describes manipulations with measurement results in the first Nyquist zone that allow the use of the Chinese remainder theorem.