scholarly journals Hilbert transform using a robust geostatistical method

2021 ◽  
Vol 942 (1) ◽  
pp. 012029
Author(s):  
O Marashly ◽  
M Dobroka
Keyword(s):  
Fourier Transform ◽  
Hilbert Transform ◽  
Test Procedure ◽  
Analytical Signal ◽  
Cauchy Distribution ◽  
Dft Method ◽  
Hermite Functions ◽  
Time Range ◽  
Time Signal ◽  
Inversion Method

Abstract In this paper, we introduced an efficient inversion method for Hilbert transform calculation which can be able to eliminate the outlier noise. The Most Frequent Value method (MFV) developed by Steiner merged with an inversion-based Fourier transform to introduce a powerful Fourier transform. The Fourier transform process (IRLS-FT) ability to noise overthrow efficiency and refusal to outliers make it an applicable method in the field of seismic data processing. In the first part of the study, we introduced the Hilbert transform stand on a efficient inversion, after that as an example we obtain the absolute value of the analytical signal which can be used as an attribute gauge. The method depends on a dual inversion, first we obtain the Fourier spectrum of the time signal via inversion, after that, the spectrum calculated via transformation of Hilbert transforms into time range using a efficient inversion. Steiner Weights is used later and calculated using the Iterative Reweighting Least Squares (IRLS) method (efficient inverse Fourier transform). Hermite functions in a series expansion are used to discretize the spectrum of the signal in time. These expansion coefficients are the unknowns in this case. The test procedure was made on a Ricker wavelet signal loaded with Cauchy distribution noise to test the new Hilbert transform. The method shows very good resistance to outlier noises better than the conventional (DFT) method.

scholarly journals Heisenberg–Weyl Groups and Generalized Hermite Functions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1060
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano A. del del Olmo
Keyword(s):  
Hilbert Space ◽  
Fourier Transform ◽  
Heisenberg Group ◽  
Real Line ◽  
Hermite Functions ◽  
Unitary Representations ◽  
Weyl Groups ◽  
The Real ◽  
Symmetry Properties ◽  
The Fourier Transform

We introduce a multi-parameter family of bases in the Hilbert space L2(R) that are associated to a set of Hermite functions, which also serve as a basis for L2(R). The Hermite functions are eigenfunctions of the Fourier transform, a property that is, in some sense, shared by these “generalized Hermite functions”. The construction of these new bases is grounded on some symmetry properties of the real line under translations, dilations and reflexions as well as certain properties of the Fourier transform. We show how these generalized Hermite functions are transformed under the unitary representations of a series of groups, including the Weyl–Heisenberg group and some of their extensions.

scholarly journals Fault Detection in DC Microgrids Using Short-Time Fourier Transform

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 277
Author(s):  
Ivan Grcić ◽  
Hrvoje Pandžić ◽  
Damir Novosel
Keyword(s):  
Fourier Transform ◽  
Fault Detection ◽  
Operating Conditions ◽  
Time Signal ◽  
Short Time Fourier Transform ◽  
Dc Microgrid ◽  
Protection Scheme ◽  
Simulink Model ◽  
Battery Energy ◽  
Short Time

Fault detection in microgrids presents a strong technical challenge due to the dynamic operating conditions. Changing the power generation and load impacts the current magnitude and direction, which has an adverse effect on the microgrid protection scheme. To address this problem, this paper addresses a field-transform-based fault detection method immune to the microgrid conditions. The faults are simulated via a Matlab/Simulink model of the grid-connected photovoltaics-based DC microgrid with battery energy storage. Short-time Fourier transform is applied to the fault time signal to obtain a frequency spectrum. Selected spectrum features are then provided to a number of intelligent classifiers. The classifiers’ scores were evaluated using the F1-score metric. Most classifiers proved to be reliable as their performance score was above 90%.

scholarly journals Hermite Functions and Fourier Series

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 853
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano del Olmo
Keyword(s):  
Fourier Transform ◽  
Hermite Functions ◽  
Quantum Oscillator ◽  
Linear Combinations ◽  
Ladder Operators ◽  
Orthonormal Bases ◽  
Integrable Functions ◽  
The Fourier Transform ◽  
The One ◽  
Square Integrable Functions

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle (L2(C)) and in l2(Z), which are related to each other by means of the Fourier transform and the discrete Fourier transform. These relations are unitary. The construction of orthonormal bases requires the use of the Gramm–Schmidt method. On both spaces, we have provided ladder operators with the same properties as the ladder operators for the one-dimensional quantum oscillator. These operators are linear combinations of some multiplication- and differentiation-like operators that, when applied to periodic functions, preserve periodicity. Finally, we have constructed riggings for both L2(C) and l2(Z), so that all the mentioned operators are continuous.

Flow-Through Fourier Transform Infrared Sensor for Total Hydrocarbons Determination in Water

2009 ◽  
Vol 63 (9) ◽  
pp. 1015-1021 ◽  
Author(s):  
David Pérez-Palacios ◽  
Sergio Armenta ◽  
Bernhard Lendl
Keyword(s):  
Fourier Transform ◽  
Limit Of Detection ◽  
Solid Phase ◽  
Chlorinated Solvents ◽  
Analytical Signal ◽  
Fourier Transform Infrared ◽  
Minimal Sample ◽  
Relative Standard ◽  
Ft Ir ◽  
Flow Through

A new flow-through Fourier transform infrared (FT-IR) sensor for oil in water analysis based on solid-phase spectroscopy on octadecyl (C18) silica particles has been developed. The C18 non-polar sorbent is placed inside the sensor and is able to retain hydrocarbons from water samples. The system does not require the use of chlorinated solvents, reducing the environmental impact, and the minimal sample handling stages serve to ensure sample integrity whilst reducing exposure of the analyst to any toxic hydrocarbons present within the samples. Fourier transform infrared (FT-IR) spectra were recorded by co-adding 32 scans at a resolution of 4 cm−1 and the band located at 1462 cm−1 due to the CH2 bending was integrated from 1475 to 1450 cm−1 using a baseline correction established between 1485 and 1440 cm−1 using the areas as analytical signal. The technique, which provides a limit of detection (LOD) of 22 mg L−1 and a precision expressed as relative standard deviation (RSD) lower than 5%, is considerably rapid and allows for a high level of automation.

Deterministic Discrete-Time Signal Transforms

2021 ◽  
pp. 714-796
Author(s):  
Stevan Berber
Keyword(s):  
Fourier Transform ◽  
Discrete Time ◽  
Linear Time ◽  
Power Spectra ◽  
Time Signal ◽  
Linear Time Invariant ◽  
Energy Spectral Density ◽  
Analysis And Synthesis ◽  
Spectral Density Functions ◽  
Linear Time Invariant Systems

Chapter 15 presents a detailed analysis of discrete-time signals and systems in the frequency domain, including the theory of the discrete Fourier series, the discrete-time Fourier transform, and the discrete Fourier transform, and key examples relevant for the analysis and synthesis of signals processed in the discrete transceiver blocks of a communication system. Amplitude spectra, magnitude spectra, phase spectra, and power spectra are defined and calculated for typical signals. Using a unique notation that distinguishes between energy signals and power signals, the correlation function and power or energy spectral density functions are inter-related by proving the Wiener–Khintchine theorem. A comprehensive analysis of linear-time-invariant systems, using the notions of impulse responses, correlation functions, and power spectral densities for both power and energy signals, is presented. The basic theory of the z-transform is also presented.

scholarly journals Computationally Efficient Sources Location Method for Nested Array via Massive Virtual Difference Co-Array

Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 1961
Author(s):  
Wei Wu ◽  
Yunfei Wang ◽  
Xiaofei Zhang ◽  
Jianfeng Li
Keyword(s):  
Fourier Transform ◽  
Parametric Method ◽  
Computational Cost ◽  
Dft Method ◽  
Doa Estimation ◽  
Practical Implementation ◽  
Computationally Efficient ◽  
Virtual Sensors ◽  
Phase Rotation ◽  
Array Aperture

In this paper, we derive the discrete Fourier transform (DFT) method for direction of arrival (DOA) estimation by generating the massive virtual difference co-array with the nested array. By contrast with the spatial smoothing (SS) subspace-based methods for nested array, which halve the array aperture, the proposed method can take full advantage of the total array aperture. Since the conventional DFT method is a non-parametric method and is limited by Rayleigh threshold, we perform the phase rotation operation to obtain the fine DOA estimates. Owing to the full utilization of the array aperture and phase rotation operation, the proposed method can achieve better performance than SS subspace-based methods for far-field sources especially with massive virtual difference co-arrays which possess a large number of virtual sensors. Besides, as the fast Fourier transform (FFT) is attractive in practical implementation, the proposed method lowers the computational cost, as compared with the subspace-based methods. Numerical simulation results validate the superiority of the proposed method in both estimation performance and complexity.

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