A Novel Sub-Nyquist FRI Sampling and Reconstruction Method in Linear Canonical Transform Domain

• DOI: 10.1007/s00034-021-01759-w
• Publication Date: 2021-06-11T21:02:15Z
• Authors: Hong-Cai Xin; Bing-Zhao Li; Xia Bai
• Keywords: Nyquist–Shannon sampling theorem; Aliasing; Nyquist rate; Oversampling; Nyquist frequency; Kernel (algebra); Signal reconstruction

The finite-rate-of-innovation (FRI) sampling frame has drawn a great deal of attention in many applications. In this paper, a novel sub-Nyquist FRI-based sampling and reconstruction method in linear canonical transform (LCT) domain is proposed. First, a new, compact-support sampling kernel is designed to acquire sub-Nyquist samples in time domain, which can be viewed as anti-aliasing prefilter in LCT domain. Then, the corresponding sampling theorem is derived and the reconstruction algorithm is summarized based on annihilating filter and least square method. Moreover, compared with other representative sub-Nyquist sampling methods, the experiment results demonstrate the superior reconstruction performance of the proposed method. The reconstruction ability in noisy environment is also measured by mean square error. Finally, the proposed method is applied to time delay estimation and can obtain super-resolution results.