Performance of reconstruction factors for a class of new complex continuous wavelets

2020 ◽  
pp. 2050067
Author(s):  
Mohammed Rayeezuddin ◽  
B. Krishna Reddy ◽  
D. Sudheer Reddy
Keyword(s):  
Morlet Wavelet ◽  
Comparative Assessment ◽  
Data Sets ◽  
Continuous Wavelet ◽  
Reconstruction Formula ◽  
Admissibility Condition ◽  
High Frequencies ◽  
Continuous Wavelets ◽  
Non Stationary Signal ◽  
Wavelet Family

In this paper, we determine the factors necessary for the reconstruction of the signal from its continuous wavelet transform performed using the new complex continuous wavelet family by making use of admissible conditions and studied some of its properties. We also make a comparative assessment of its performance with the existing complex continuous wavelets, such as Morlet, Paul and DOG, in terms of reconstruction capability. The reconstruction was performed on three data sets, namely, a signal with a mixture of low and high frequencies, a non-stationary signal (synthetic) and an ECG signal. The results show that the proposed family of wavelets reconstruction capability is comparable with Morlet, Paul and DOG wavelets. Further, we investigate an alternate reconstruction formula without making use of admissibility condition and compare its efficiency of reconstruction with the standard (restricted) Morlet wavelet.

scholarly journals On alternative wavelet reconstruction formula: a case study of approximate wavelets

2014 ◽  
Vol 1 (2) ◽  
pp. 140124 ◽  
Author(s):  
Elena A. Lebedeva ◽  
Eugene B. Postnikov
Keyword(s):  
Wavelet Transform ◽  
Wide Class ◽  
Continuous Wavelet Transform ◽  
Morlet Wavelet ◽  
Continuous Wavelet ◽  
Reconstruction Formula ◽  
Physical Processes ◽  
Admissibility Condition ◽  
Oscillatory Dynamics

The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed.

scholarly journals A wavelet neural control scheme for a quadrotor unmanned aerial vehicle

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170248 ◽  
Author(s):  
F. Jurado ◽  
S. Lopez
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Unmanned Aerial Vehicle ◽  
Continuous Wavelet Transform ◽  
Morlet Wavelet ◽  
Wavelet Neural Network ◽  
Continuous Wavelet ◽  
Continuous Wavelets ◽  
Control Scheme ◽  
Aerial Vehicle

Wavelets are designed to have compact support in both time and frequency, giving them the ability to represent a signal in the two-dimensional time–frequency plane. The Gaussian, the Mexican hat and the Morlet wavelets are crude wavelets that can be used only in continuous decomposition. The Morlet wavelet is complex-valued and suitable for feature extraction using the continuous wavelet transform. Continuous wavelets are favoured when high temporal and spectral resolution is required at all scales. In this paper, considering the properties from the Morlet wavelet and based on the structure of a recurrent high-order neural network model, a novel wavelet neural network structure, here called a recurrent Morlet wavelet neural network, is proposed in order to achieve a better identification of the behaviour of dynamic systems. The effectiveness of our proposal is explored through the design of a decentralized neural backstepping control scheme for a quadrotor unmanned aerial vehicle. The performance of the overall neural identification and control scheme is verified via simulation and real-time results. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

scholarly journals Метод трансляционного переноса для оценки стабильности нестационарного квантового стандарта частоты

2021 ◽  
Vol 91 (1) ◽  
pp. 32
Author(s):  
С.В. Божокин ◽  
К.А. Баранцев ◽  
А.Н. Литвинов
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Frequency Standard ◽  
Continuous Wavelet ◽  
Quantum Frequency ◽  
Quantum Frequency Standard ◽  
Standard Signal ◽  
Wavelet Variance ◽  
Non Stationary Signal

Continuous wavelet transform is used to analyze the operation of a non-stationary signal of a quantum frequency standard. The method of translational transfer is proposed, with the help of which the boundary phenomena in this transformation are eliminated. The spectral integrals of the quantum frequency standard signal in various frequency ranges are calculated. A wavelet dispersion is introduced, which makes it possible to determine the moments of time when the signal fluctuations are the strongest. The comparison of the wavelet variance with the usual variance and with the Allen variance is carried out.

The use of a continuous wavelet transform in the diagnostics of technical condition of a shock absorber built in automotive vehicle

2018 ◽  
Vol 121 ◽  
pp. 171-179
Author(s):  
Łukasz Konieczny ◽  
Rafał Burdzik
Keyword(s):  
Wavelet Transform ◽  
Shock Absorber ◽  
Technical Condition ◽  
Morlet Wavelet ◽  
Continuous Wavelet ◽  
Nonlinear Characteristics ◽  
Shock Absorbers ◽  
Acceleration Sensors ◽  
Research Experiment ◽  
Difficult Issue

Diagnosing the technical condition of shock absorbers installed in automotive suspensions is a difficult issue due to the fact that these are elements of a complex mechanical system containing elastic and damping elements with nonlinear characteristics that degrade during operation. The paper presents the result of testing car with shock absorbers with programmed faults on the harmonic stand. The test object was a Fiat Seicento passenger car. The research experiment consisted in stimulating the vehicle to vibrations of forced masses, unsprung and sprung, and registration of vibration accelerations of these masses. The tests were subjected to shock absorbers with programmed faults in the form of loss of shock absorber fluid from 100% to 35% for rear shock absorbers. The acceleration of plates, swingarm (unsprung masses) and bodywork (sprung masses) were recorded by acceleration sensors. The results obtained in this way were subjected to wavelet analysis using the Morlet wavelet in the MatLab environment and based on these transformations the maximum of vibration amplitudes were determined depending on the degree of loss of the shock absorber fluid.

Amplitude and phase correction of helicopter EM data

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. F119-F126 ◽  
Author(s):  
Yusen Ley-Cooper ◽  
James Macnae
Keyword(s):  
Half Space ◽  
Low Frequency ◽  
Earth Model ◽  
Data Sets ◽  
High Frequencies ◽  
Electromagnetic Data ◽  
Historic Data ◽  
Case Data ◽  
Best Fit ◽  
Deep Sediments

We aim to develop a quantitative method for recalibration of historic helicopter electromagnetic data sets. Recent research has shown that frequency-domain helicopter electromagnetic data collected over a conductive half-space such as calm seawater can be used to correct system calibration errors. However, most historic surveys consist only of data collected over land, where the conductive half-space assumption is rarely justified. We estimate the required recalibration parameters by analyzing systematic misfits in the inversion of statistically chosen measures of historic data. Our method requires the identification, within the survey area, of a zone of conductive responses that are reasonably uniform. From this zone, a set of altitude-corrected median responses are estimated. These are inverted using geologically specifiedconstraints to obtain a best-fit layered earth model. Systematic inconsistencies between the median measured altitude and the inverted depth to surface are attributed to altitude error. Remaining frequency-dependent fitting errors are assumed to be the calibration errors. We tested the method with partial success on helicopter electromagnetic data sets collected over uniform deep sediments where seawater data were also available and two different inland surveys over multiple lithologies in one general area. At high frequencies, our method works reliably. Recalibration of low-frequency data is not possible if the area used as a reference consists of moderate or poor conductors. In this case, data amplitudes are small and are greatly affected by imperfect drift and magnetic susceptibility corrections. Historic helicopter electromagnetic data may require amplitude rescaling up to 20%–30%, with phase shifts of up to 3°.

scholarly journals APPLICATION OF ISO-FREQUENCY MAPS TO TIME-LAPSE DATA

2017 ◽  
Vol 35 (3) ◽  
Author(s):  
Wagner Moreira Lupinacci ◽  
Anderson Peixoto de Franco ◽  
Fernando Vizeu Santos ◽  
Marco Antonio Cetale Santos
Keyword(s):  
Wavelet Transform ◽  
Energy Density ◽  
Curvelet Transform ◽  
Time Lapse ◽  
Morlet Wavelet ◽  
Seismic Exploration ◽  
Time Frequency ◽  
Advantages And Disadvantages ◽  
Morlet Wavelet Transform ◽  
Non Stationary Signal

ABSTRACT. Time-frequency transforms are widely used in seismic exploration. These transforms enable analysis of the energy density of a non-stationary signal as functions of amplitude, time and frequency. The representation of energy density is not unique, and each transform has its advantages and disadvantages. The choice of which transform should be used depends on the application. In this paper, we propose a new way to analyze time-lapse anomalies using iso-frequency panels obtained by time-frequency transforms. We compared the iso-frequency panels of the Morlet Wavelet Transform and Choi-Williams Distribution. These panels revealed different characteristics and can provide additional information for the interpretation of time-lapse anomalies. We used seismic data from the Marimbá field of the Campos Basin, Brazil, for which base and monitor acquisitions were held in 1984 and 1999, respectively. We also used a special filtering approach to enhance seismic resolution and remove noise, whereby we applied the curvelet transform to remove noise, and employed a tool to correct the residual moveout and inverse Q filtering for attenuation correction. Then we analysed the time-lapse anomalies using iso-frequency panels. The main time-lapse anomalies appeared in the form of clouds in the iso-frequency panels obtained by the Morlet Wavelet Transform approach. Iso-frequency panels obtained by Choi-Williams Distribution showed a higher sensitivity and resolution for analyzing the anomalies. Our results show the great potential of these transforms for visualization of time-lapse anomalies. Keywords: time-lapse anomalies, spectrogram, Morlet Wavelet Transform, Choi-Williams Distribution. RESUMO. Transformadas tempo-frequência são amplamente utilizadas na exploração sísmica. Estas transformadas permitem a análise da densidade de energia de um sinal não-estacionário como funções de amplitude, tempo e frequência. A representação da densidade de energia de um sinal não é única, e cada transformada tem suas vantagens e desvantagens. A escolha da transformada que deve ser usada depende da aplicação. Neste artigo, propomos uma nova abordagem para analisar anomalias de dados time-lapse usando painéis iso-frequência obtidos através de transformadas tempo-frequência. Comparamos os painéis iso-frequência obtidos com a Transformada Wavelet de Morlet e a Distribuição de Choi-Williams. Estes painéis revelaram diferentes características que podem fornecer informações adicionais para a interpretação de anomalias time-lapse. Os dados sísmicos utilizados foram do Campo de Marimbá da Bacia de Campos, Brasil, os quais as aquisições base e monitor foram realizadas em 1984 e 1999, respectivamente. Antes da análise dos painéis iso-frequência, usamos um workflow para melhorar a resolução sísmica e a razão sinal-ruído. Neste workflow, aplicamos a Transformada Curvelet para remover ruídos aleatórios e coerentes, uma ferramenta para corrigir o moveout residual e um Q-filter para correção dos efeitos da atenuação. Após este workflow, as principais anomalias time-lapse apareceram na forma de nuvens nos painéis iso-frequência da Transformada Wavelet de Morlet. Já os painéis iso-frequência da Distribuição de Choi-Williams apresentaram uma maior sensibilidade e resolução para análise dessas anomalias. Os resultados mostraram o grande potencial dessas transformadas para a visualização e interpretação de anomalias time-lapse. Palavras-chave: anomalias time-lapse, espectrograma, Transformada Wavelet de Morlet, Distribuição Choi-Williams. 

scholarly journals Twitter as an innovation process with damping effect

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Giacomo Aletti ◽  
Irene Crimaldi
Keyword(s):  
Frequency Distribution ◽  
Power Law ◽  
Empirical Data ◽  
General Model ◽  
Innovation Process ◽  
Data Sets ◽  
High Frequencies ◽  
Damping Effect ◽  
Twitter Data ◽  
Innovation Processes

AbstractIn the existing literature about innovation processes, the proposed models often satisfy the Heaps’ law, regarding the rate at which novelties appear, and the Zipf’s law, that states a power law behavior for the frequency distribution of the elements. However, there are empirical cases far from showing a pure power law behavior and such a deviation is mostly present for elements with high frequencies. We explain this phenomenon by means of a suitable “damping” effect in the probability of a repetition of an old element. We introduce an extremely general model, whose key element is the update function, that can be suitably chosen in order to reproduce the behaviour exhibited by the empirical data. In particular, we explicit the update function for some Twitter data sets and show great performances with respect to Heaps’ law and, above all, with respect to the fitting of the frequency-rank plots for low and high frequencies. Moreover, we also give other examples of update functions, that are able to reproduce the behaviors empirically observed in other contexts.

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