In this paper we define a new compact Hilbert index which, while maintaining all of the advantages of the standard Hilbert curve, permits spaces with unequal dimension cardinalities. The compact Hilbert index can be used in any application that would have previously relied on Hilbert curves but, in the case of unequal side lengths, provides a more memory efficient representation. This advantage...

A novel data-driven modal analysis method, reduced-order variational mode decomposition (RVMD), is proposed, inspired by the Hilbert–Huang transform and (VMD), to resolve transient or statistically non-stationary flow dynamics. First, form of RVMD modes (referred as an ‘elementary low-order dynamic process’, ELD) constructed combining representation idea intrinsic function, which enables comput...

The electric power systems together with the entire energy sector are rapidly evolving towards a low-carbon, secure, and competitive economy facing revolutionary transformations from technical structure to economic value chain. Pathways achieve sustainability led development of new technologies, accommodation larger shares unpredictable stochastic electricity transfer sources end-users without ...

We give an operator theoretic approach to the constructions of multiresolutions as they are used in a number of basis constructions with wavelets, and in Hilbert spaces on fractals. Our approach starts with the following version of the classical Baumslag-Solitar relations ut = tu where t is a unitary operator in a Hilbert space H and u is an isometry in H. There are isometric dilations of this ...

In this article, we throw a bridge between two objects which are unrelated at rst sight. One is the in nite dimensional Heisenberg algebra (simply the Heisenberg algebra, later) which plays a fundamental role in the representation theory of the a ne Lie algebras. The other is the Hilbert schemes of points on a complex surface appearing in the algebraic geometry. As we will explain soon, the Hei...

Huang’s Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal’s instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be...

Unbalance, fatigue crack and rotor-stator rub are the three common and important faults in a rotor-bearing system. They are originally interconnected each other, and their vibration behaviors do often show strong nonlinear and transient characteristic, especially when more than one of them coexist in the system. This article is aimed to study the vibration response of the rotor system in presen...

We propose Hilbert transform and analytic signal construction for signals over graphs. This is motivated by the popularity of Hilbert transform, analytic signal, and modulation analysis in conventional signal processing, and the observation that complementary insight is often obtained by viewing conventional signals in the graph setting. Our definitions of Hilbert transform and analytic signal ...