Search results for "Hilbert transform"

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…

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…

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…

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…

Rectifiability and singular integrals

1995

Inversion Formulas for the Discretized Hilbert Transform on the Unit Circle

1998

A discrete version of the Hilbert transform on the unit circle is considered. Its Moore--Penrose inverse with respect to suitable scalar products is derived for different side conditions. Furthermore, stability of the pseudo-inverse is studied. These results allow the efficient computation of approximate solutions of singular integral equations with Hilbert kernel. Furthermore, the stability analysis of such methods becomes much easier even for graded meshes which are useful for weakly singular solutions.

Incipient damage identification through characteristics of the analytical signal response

2008

The analytical signal is a complex representation of a time domain signal: the real part is the time domain signal itself, while the imaginary part is its Hilbert transform. It has been observed that damage, even at a very low level, yields clearly detectable variations of analytical signal quantities such as phase and instantaneous frequency. This observation can represent a step toward a quick and effective tool to recognize the presence of incipient damage where other frequency-based techniques fail. In this paper a damage identification procedure based on an adimensional functional of the square of the difference between the characteristics of the analytical theoretical and measured sig…

A damage identification procedure based on Hilbert transform: Experimental validation

2010

SUMMARY This paper aims at validating the feasibility of an identification procedure, based on the use of the Hilbert transform, by means of experimental tests for shear-type multi-degree-of-freedom systems. Particularly, a three-degree-of-freedom frame will be studied either numerically or experimentally by means of a laboratory scale model built at the laboratory of the Structural, Aerospace and Geotechnical Engineering Department (DISAG) of University of Palermo. Several damage scenarios have been considered to prove the effectiveness of the procedure. Moreover, the experimental tests have been conducted by considering two different input loads: pulse forces, simulated by means of an ins…

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 …

The Study of Dynamic Objects Identification Algorithms Based on Anisotropic Properties of Generalized Amplitude-Phase Images

2018

The article presents some results of dynamical objects identification technology based on coincidence matrixes of templates and tested objects’ amplitude-phase images (APIm) calculated with discrete Hilbert transforms (DHT). DHT algorithms are modeled on basis of isotropic (HTI), anisotropic (HTA), generalized transforms – AP-analysis (APA) and the difference (residual) relative shifted phase (DRSP-) images to calculate the APIm. The identified objects are recognized as members of classes modeled with 3D templates – images of different types airplanes rotated in space. The dynamic anisotropic properties of APIm causes the increasing of sensitivity to circular angle rotation and make possibl…