Regularized Sampling of Multiband Signals
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 and perturbations 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 elements corresponding to the multiband components. It is shown that this method can be well combined with the recently proposed synchronous multirate 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.