Fractal functions and wavelet expansions based on several scaling functions
Journal of Approximation Theory
Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Uncertainty relations for shift-invariant analog signals
IEEE Transactions on Information Theory
Time-delay estimation from low-rate samples: a union of subspaces approach
IEEE Transactions on Signal Processing
Higher order sampling and recovering of lowpass signals
IEEE Transactions on Signal Processing
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors
IEEE Transactions on Signal Processing - Part I
| Hi-index | 35.68 |
The problem of recovering a signal from its low frequency components occurs often in practical applications due to the lowpass behavior of many physical systems. Here, we study in detail conditions under which a signal can be determined from its low-frequency content. We focus on signals in shift-invariant spaces generated by multiple generators. For these signals, we derive necessary conditions on the cutoff frequency of the lowpass filter as well as necessary and sufficient conditions on the generators such that signal recovery is possible. When the lowpass content is not sufficient to determine the signal, we propose appropriate pre-processing that can improve the reconstruction ability. In particular, we show that modulating the signal with one or more mixing functions prior to lowpass filtering, can ensure the recovery of the signal in many cases, and reduces the necessary bandwidth of the filter.