Sub-Nyquist Sampling of Multiple Exponentially Damped Sinusoids With Feedback Structure

Multiple exponentially damped sinusoids (MEDS) signals have been widely applied to the fields of speech analysis and nuclear magnetic resonance imaging systems. Although sub-Nyquist sampling schemes were proposed in previous works, either the image frequency aliasing was not resolved or the parameters measuring process required a large number of samples. In this article, a feedback-based sub-Nyquist sampling and parameters measurement scheme for MEDS signals is proposed to address these problems. Since sub-Nyquist sampling would lead to frequencies ambiguity, an additional sampling is designed to determine the true frequencies. Moreover, image frequency aliasing would occur when the difference between two true frequencies is an integer multiple of the sampling rate. To prevent image frequency aliasing, a feedback sampling strategy and a dealiasing algorithm are proposed. The proposed scheme enables the sub-Nyquist sampling and parameters measurement of MEDS signals with
$K$
frequency components by using only
$4K$
samples. We also propose a hardware prototype to implement the proposed system. Simulation and hardware experiment results have shown that the frequency estimation accuracy of the proposed method has been improved on average by about 11.65 dB than previous works under noise environment, and the statistical variance experiments have shown that it has better stability.