Nyquist Pulses for Sub-Nyquist Sampling — Application to Underwater Imaging

Abstract

The introduction of finite-rate-of-innovation (FRI) sampling has made it possible to sample and perfectly reconstruct certain classes of non-bandlimited signals. The design of sampling kernels for FRI framework relies on frequency-domain alias-cancellation and Strang-Fix conditions. We establish an equivalence between the alias-cancellation conditions and zero intersymbol interference (ISI) conditions required for distortionless transmission in the field of digital communication. Consequently, Nyquist pulses employed for ISI-free communication could also be used as FRI sampling kernels. As an example, a Nyquist pulse, namely, the raised-cosine pulse is employed as the FRI sampling kernel and its performance is analyzed in the presence of noise. In essence, we show that any admissible FRI sampling kernel follows the Nyquist pulse criterion and can be used interchangeably. As an application, we demonstrate super-resolution underwater imaging by employing the FRI signal model on experimental active sonar measurements. Compared with standard matched filtering, the FRI methodology results in superior-quality image reconstruction.