Search results for "Hilbert Transform"
showing 10 items of 24 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 …
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…
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…
Exponential instability in the fractional Calder\'on problem
2017
In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on pro…
Methods of Digital Hilbert Optics in the Analysis and Objects’ Recognition
2016
This paper describes methods on how to increase the effectiveness of objects’ pictures identification based on correlation methods. The main concept of increasing the discriminant effectiveness is based on highlighting of characteristic points of recognized objects by applying Hilbert transformations. Study of the effectiveness of Digital Hilber Optics (DHO) have been performed on a set of aircrafts, whose models rendered first as binary images, and then as grayscale. It has been performed a very detailed analysis of requirements on resources of information system’s which would in a real world support the discriminatory decision of objects’ class for which the sample database has been creat…
An Innovative Ambient Identification Method
2020
Ambient modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method based on appl…
Fast fringe pattern phase demodulation using FIR Hilbert transformers
2016
This paper suggests the use of FIR Hilbert transformers to extract the phase of fringe patterns. This method is computationally faster than any known spatial method that produces wrapped phase maps. Also, the algorithm does not require any parameters to be adjusted which are dependent upon the specific fringe pattern that is being processed, or upon the particular setup of the optical fringe projection system that is being used. It is therefore particularly suitable for full algorithmic automation. The accuracy and validity of the suggested method has been tested using both computer-generated and real fringe patterns. This novel algorithm has been proposed for its advantages in terms of com…
A novel identification procedure from ambient vibration data
2020
AbstractAmbient vibration modal identification, also known as Operational Modal Analysis, aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method b…