The primary goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients. This problem is important to several areas of research in signal processing, especially speech recognition technology, as well as state tomography in quantum theory. We present linear reconstruction algorithms for tight frames associated with projective 2-designs in fini...

Estimating local dynamic stability is considered a powerful approach to identify persons with balance impairments. Its validity has been studied extensively, and provides evidence that short-term local dynamic stability is related to balance impairments and the risk of falling. Thus far, however, this relation has only been proven on group level. For clinical use, differences on the individual ...

A general protocol in quantum information and communication relies in the ability of producing, transmitting, and reconstructing, in general, qunits. In this Letter we show for the first time the experimental implementation of these three basic steps on a pure state in a three-dimensional space, by means of the orbital angular momentum of the photons. The reconstruction of the qutrit is perform...

Times series obtained from dynamical systems can be converted into sequences of time intervals between relevant events. We show that under quite general conditions time intervals are phase space observables and therefore embedding theorems for the reconstruction of a state space from scalar signals are valid. The practical applicability in data analysis is discussed with the help of numerical a...

In this study, a mixed 2 filter design is proposed for multirate transmultiplexer systems with dispersive channel and additive noise. First, a multirate state-space representation is introduced for the transmultiplexer with the consideration of channel dispersion. Then, the problem of signal reconstruction can be regarded as a state estimation problem. In order to design an efficient separating...

The standard state-spaces of asymmetric information preclude non-trivial forms of unawareness (Modica and Rustichini, 1994, Dekel, Lipman and Rustichini, 1998). We introduce a generalized state-space model that allows for non-trivial unawareness among several individuals, and which satisfies strong properties of knowledge as well as all the desiderata on unawareness proposed this far in the lit...

We are often interested in finding out if a given predicate on states of a system can be satisfied in any or all of the systems reachable states. To determine this, one approach is to calculate the complete set of reachable states and evaluate the predicate on each of these states. To know which states we have already examined and which we have yet to examine—and thus knowing when we have exami...