Regularized sampling of multiband signals

TL;DR

This paper introduces a regularized sampling technique for multiband signals that approaches the Landau limit with low noise sensitivity, combining band-limited windowing and trigonometric approximation, suitable for various signal types.

Contribution

It proposes a novel regularized sampling method that inherits multiband properties and can be integrated with SMRS, improving efficiency and noise robustness in multiband signal processing.

Findings

Method approaches Landau limit with low noise sensitivity.

Compatible with sparse linear systems in SMRS scheme.

Effective for bounded, unbounded energy, and periodic signals.

Abstract

This paper presents a regularized sampling method for multiband signals, that makes it possible to approach the Landau limit, while keeping the sensitivity to noise at a low level. The method is based on band-limited windowing, followed by trigonometric approximation in consecutive time intervals. The key point is that the trigonometric approximation "inherits" the multiband property, that is, its coefficients are formed by bursts of non-zero elements corresponding to the multiband components. It is shown that this method can be well combined with the recently proposed synchronous multi-rate sampling (SMRS) scheme, given that the resulting linear system is sparse and formed by ones and zeroes. The proposed method allows one to trade sampling efficiency for noise sensitivity, and is specially well suited for bounded signals with unbounded energy like those in communications, navigation, audio systems, etc. Besides, it is also applicable to finite energy signals and periodic band-limited signals (trigonometric polynomials). The paper includes a subspace method for blindly estimating the support of the multiband signal as well as its components, and the results are validated through several numerical examples.