On distributed sampling of smooth non-bandlimited fields
Proceedings of the 3rd international symposium on Information processing in sensor networks
Adaptive reference levels in a level-crossing analog-to-digital converter
EURASIP Journal on Advances in Signal Processing
On the accuracy and resolution of powersum-based sampling methods
IEEE Transactions on Signal Processing
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
IEEE Transactions on Image Processing
Performance analysis of a flexible subsampling receiver for pulsed UWB signals
IEEE Transactions on Wireless Communications
IEEE Transactions on Image Processing
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
SARNOFF'09 Proceedings of the 32nd international conference on Sarnoff symposium
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Sampling piecewise sinusoidal signals with finite rate of innovation methods
IEEE Transactions on Signal Processing
Distributed sampling for dense sensor networks: a "Bit-conservation principle"
IPSN'03 Proceedings of the 2nd international conference on Information processing in sensor networks
Distributed sampling of signals linked by sparse filtering: theory and applications
IEEE Transactions on Signal Processing
Time-delay estimation from low-rate samples: a union of subspaces approach
IEEE Transactions on Signal Processing
Beyond Nyquist: efficient sampling of sparse bandlimited signals
IEEE Transactions on Information Theory
Compressive sampling of EEG signals with finite rate of innovation
EURASIP Journal on Advances in Signal Processing
Sampling and reconstruction of transient signals by parallel exponential filters
IEEE Transactions on Circuits and Systems II: Express Briefs
Space-time-frequency processing of acoustic wave fields: theory, algorithms, and applications
IEEE Transactions on Signal Processing
Single antenna power measurements based direction finding
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Randomization of data acquisition and l1-optimization (recognition with compression)
Automation and Remote Control
Two-dimensional random projection
Signal Processing
Advances in Computational Mathematics
High-resolution ranging method based on low-rate parallel random sampling
Digital Signal Processing
Representation of sparse Legendre expansions
Journal of Symbolic Computation
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The authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials. Even though these signals are not bandlimited, we show that they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theorems for classes of signals and kernels that generalize the classic "bandlimited and sinc kernel" case. In particular, we show how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinite-length signals with finite local rate of innovation, we show local sampling and reconstruction based on spline kernels. The key in all constructions is to identify the innovative part of a signal (e.g., time instants and weights of Diracs) using an annihilating or locator filter: a device well known in spectral analysis and error-correction coding. This leads to standard computational procedures for solving the sampling problem, which we show through experimental results. Applications of these new sampling results can be found in signal processing, communications systems, and biological systems