Search results for "Hilbert"
showing 10 items of 331 documents
Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method.
2021
Abstract Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is one of the methods that have been used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described, and it is briefly compared with other commonly used frequency extraction methods. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytical…
Cross-correlation of whitened vibration signals for low-speed bearing diagnostics
2019
Abstract Rolling-element bearings are crucial components in all rotating machinery, and their failure will initially degrade the machine performance, and later cause complete shutdown. The period between an initial crack and complete failure is short due to crack propagation. Therefore, early fault detection is important to avoid unexpected machine shutdown and to aid in maintenance scheduling. Bearing condition monitoring has been applied for several decades to detect incipient faults at an early stage. However, low-speed conditions pose a challenge for bearing fault diagnosis due to low fault impact energy. To reliably detect bearing faults at an early stage, a new method termed Whitened …
Data-based modeling and estimation of vehicle crash processes in frontal fixed-barrier crashes
2017
Abstract As a complex process, vehicle crash is challenging to be described and estimated mathematically. Although different mathematical models are developed, it is still difficult to balance the complexity of models and the performance of estimation. The aim of this work is to propose a novel scheme to model and estimate the processes of vehicle-barrier frontal crashes. In this work, a piecewise model structure is predefined to represent the accelerations of vehicle in frontal crashes. Each segment in the model is corresponding to the energy absorbing component in the crashworthiness structure. With the help of Ensemble Empirical Mode Decomposition (EEMD), a robust scheme is proposed for …
Identification of Objects Based on Generalized Amplitude-Phase Images Statistical Models
2017
The article presents the dynamical objects identification technology based on statistical models of amplitude-phase images (APIm) – multidimensional data arrays (semantic models) and statistical correlation analysis methods using the generalized discrete Hilbert transforms (DHT) – 2D Hilbert (Foucault) isotropic (HTI), anisotropic (HTA) and total transforms – AP-analysis (APA) to calculate the APIm. The identified objects are modeled with 3D airplanes templates rotated in space around the center of Cartesian coordinate system. The DHT domain system of coordinates displaying the plane projections (2D flat images) remains to be space-invariant. That causes the anisotropic properties of APIm a…
A numerical property of Hilbert functions and lex segment ideals
2017
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the Osequences and encode some information about lex segment ideals. Moreover, we introduce numerical functions called fractal functions, and we use them to solve the open problem of the classification of the Hilbert functions of any bigraded algebra.
On the Betti numbers of three fat points in P1 × P1
2019
In these notes we introduce a numerical function which allows us to describe explicitly (and nonrecursively) the Betti numbers, and hence, the Hilbert function of a set Z of three fat points whose support is an almost complete intersection (ACI) in P1 × P1 . A nonrecursively formula for the Betti numbers and the Hilbert function of these configurations is hard to give even for the corresponding set of five points on a special support in P2 and we did not find any kind of this result in the literature. Moreover, we also give a criterion that allows us to characterize the Hilbert functions of these special set of fat points.
Frame-related Sequences in Chains and Scales of Hilbert Spaces
2022
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame se…
Frames and weak frames for unbounded operators
2020
In 2012 G\u{a}vru\c{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this article we revisit these concepts for an unbounded and densely defined operator $A:\mathcal{D}(A)\to\mathcal{H}$ in two different ways. In one case we consider a non-Bessel sequence where the coefficient sequence depends continuously on $f\in\mathcal{D}(A)$ with respect to the norm of $\mathcal{H}$. In the other case we consider a Bessel sequence and the coefficient sequence depends continuously on $f\in\mathcal{D}(A)$ with respect to the graph norm of $A$.
On singular integral and martingale transforms
2007
Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on the X-valued L^p-space on the plane. Moreover, replacing equality by a linear equivalence, this is found to be the typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given.
Design and Implementation of a Data Acquisition System for R Peak Detection in Electrocardiograms
2018
This paper presents a data acquisition system for the R peak detection in electrocardiograms. R wave is one of the most important sections of the QRS complex, which has an essential role in diagnosis of heart rhythm irregularities. This paper employs Hilbert transform and adaptive threshold technique for the detection of R-peak. The performance of the system was tested using standard ECG waveform records from the MIT-BIH arrhythmia database. In addition, tests were carried out using the sensors Single Lead Heart Rate Monitor for real-time data processing Design and Implementation of a Data Acquisition System for R Peak Detection in Electrocardiograms | Request PDF. Available from: https://w…