Analog-to-information conversion for nonstationary signals

Qiang Wang, Chen Meng, Cheng Wang
2020 IEEE Access  
In this paper, we consider the problem of analog-to-information conversion for nonstationary signals, which exhibit time-varying properties with respect to spectral contents. Nowadays, sampling for nonstationary signals is mainly based on Nyquist sampling theorem or signal-dependent techniques. Unfortunately, in the context of the efficient 'blind' sampling, these methods are infeasible. To deal with this problem, we propose a novel analog-to-information conversion architecture to achieve the
more » ... re to achieve the sub-Nyquist sampling for nonstationary signals. With the proposed scheme, we present a multi-channel sampling system to sample the signals in time-frequency domain. We analyze the sampling process and establish the reconstruction model for recovering the original signals. To guarantee the wide application, we establish the completeness under the frame theory. Besides, we provide the feasible approach to simplify the system construction. The reconstruction error for the proposed system is analyzed. We show that, with the consideration of noises and mismatch, the total error is bounded. The effectiveness of the proposed system is verified in the numerical experiments. It is shown that our proposed scheme outperforms the other sampling methods state-of-the-art. INDEX TERMS Analog-to-information conversion, compressive sensing, nonstationary signals, sub-Nyquist, time-frequency. CS is a novel framework for signal processing. Under this scheme, compressive measurements are conducted to acquire 'just enough' samples that guarantee the perfect recovery of the signal of interest. In essence, CS fuses sampling and compression, instead of sampling signals at the Nyquist rate followed by conventional data compression. Then the original signals can be recovered accurately by exploring the sparsity in transform domain [8] . CS has the potential to acquire signals well-below the Nyquist rate, which may lead to significant reduction in the sampling costs, power consumption, and hardware requirement. As a consequence, CS is commonly believed to be a panacea for wideband signals to achieve the efficient sampling [9], [10]. A. CHALLENGES FOR NONSTATIONARY SIGNALS Many signals in nature and man-made systems exhibit timevarying properties. Such waveforms are called time-varying or nonstationary signals. They are encountered in various areas such as audio signals, synthetic aperture radar, and machinery [9], [11], [12] . Recent advances dealing with nonstationary signals mainly focus on the time-frequency analysis methods, since the signals are intrinsically sparse on the time-frequency plane. The main goals of suitable methods VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
doi:10.1109/access.2020.3011032 fatcat:6codhsms2rcapmpchi2iuk3qmy