The rapid increase of non-linear loads in the last three decades has caused electrical quantities such as voltages and currents in 3-phase distribution systems to become distorted waveforms. This paper reviews, explains and discusses some new concepts, definitions and new available theory in the unbalanced and distorted systems. The usefulness of the proposed practical definitions is investigat...

We make a detailed study of norm retrieval. We give several classification theorems for norm retrieval and give a large number of examples to go with the theory. One consequence is a new result about Parseval frames: If a Parseval frame is divided into two subsets with spans W1, W2 and W1 ∩W2 = {0}, then W1 ⊥W2.

Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and a constraint is chosen from C also uniformly at random. This procedure is repeated m times independently. We ask the following question: is the resulting li...

In this paper, we develop a framework of generalized phase retrieval in which one aims to reconstruct a vector x in R or C through quadratic samples x∗A1x, . . . ,x ∗ANx. The generalized phase retrieval includes as special cases the standard phase retrieval as well as the phase retrieval by orthogonal projections. We first explore the connections among generalized phase retrieval, low-rank matr...

A model of motion detection is presented. The model contains three stages. The first stage is unoriented and is selective for contrast polarities. The next two stages work in parallel. A phase insensitive stage pools across different contrast polarities through a spatiotemporal filter and thus can detect first and second order motion. A phase sensitive stage keeps contrast polarities separate, ...

This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the properties of linear phase shifts in the spherical harmonic domain, which suggest a mechanism for constructing finiteimpulse-response (FIR) filters. We show that...

We propose a framework for inversion-based estimation of certain categories of faults in discrete-time linear systems. First, we develop a novel methodology for direct estimation of unknown inputs by using only measurements of either minimum or non-minimum phase systems as well as systems with transmission zeros on the unit circle. The unknown input is reconstructed from its projections onto tw...

A linear phase correction model has been shown to accurately reflect the corrective processes involved in synchronising motor actions to an external rhythmic cue. The model originated from studies of finger tapping to an isochronous metronome beat and is based on the time series of asynchronies between the metronome and corresponding finger tap onsets, along with their associated intervals. Ove...