LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Spectrum-blind minimum-rate sampling and reconstruction of multiband signals
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 03
Optimal variable fractional delay filters in time-domain L-infinity norm
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Functionally weighted lagrange interpolation of band-limited signals from nonuniform samples
IEEE Transactions on Signal Processing
Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
Multirate synchronous sampling of sparse multiband signals
IEEE Transactions on Signal Processing
Beyond Nyquist: efficient sampling of sparse bandlimited signals
IEEE Transactions on Information Theory
Interpolation of Bounded Bandlimited Signals and Applications
IEEE Transactions on Signal Processing
Optimal sub-Nyquist nonuniform sampling and reconstruction formultiband signals
IEEE Transactions on Signal Processing
Sparse solutions to linear inverse problems with multiple measurement vectors
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing - Part I
Minimum rate sampling and reconstruction of signals with arbitrary frequency support
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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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.