Short-Observation Measurement of Multiple Sinusoids With Multichannel Sub-Nyquist Sampling

Measurement of multiple sinusoidal signals (MSSs) is significant in instrumentation and measurement, radar, communications, and many other electric systems. Measurement methods based upon Shannon sampling theory require very high sampling rates and heavy processing to estimate the frequencies and amplitudes. In this article, we propose a multichannel time-staggered sampling system to measure MSSs with short-observation sub-Nyquist samples. The sampling scheme is composed of N' time-staggered sampling channels, where the staggered time is allowed to be greater than the Nyquist sampling interval. The estimation method is based on the frequency domain sparse common support (SCS) model and the Chinese remainder theorem (CRT). To estimate K frequency components in the signal without image frequency aliasing, N' \geq 2 sampling channels and N\geq \lceil K+K/N' \rceil samples for each channel are enough. In the situation when image frequency aliasing exists, N' \geq 2K and N\geq 2K samples are sufficient. We further explore the analysis of noisy signals and generalize our proposal to real-valued signals. Simulation and hardware experimental results demonstrate the effectiveness and robustness of the proposed method.