Signal recovery from low frequency components

In many applications only the low frequency components of a signal can be measured due to the lowpass behavior of many physical systems. Nevertheless, if additional information on the structure of the signal is known, it might still be possible to reconstruct the signal from its low-frequency content. This paper studies signals in shift-invariant spaces with multiple generators and derives necessary conditions on the band with of the lowpass filter as well as sufficient conditions on the generators such that signal recovery is possible. If the signal can not be recovered from its low frequency components, an appropriate pre-processing of the signal is proposed which improves the reconstruction ability. In particular, it is shown that modulating the signal with one or more mixing functions prior to lowpass filtering can ensure the recovery of the signal in many cases.