scholarly journals An algorithm to simulate nonstationary and non-Gaussian stochastic processes

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
H. P. Hong ◽  
X. Z. Cui ◽  
D. Qiao
Keyword(s):  
Fourier Transform ◽  
Stochastic Processes ◽  
Wavelet Transforms ◽  
Spectral Density Function ◽  
Transform Domain ◽  
Amplitude Correction ◽  
Power Spectral ◽  
S Transform ◽  
The Fourier Transform ◽  
Non Gaussian

AbstractWe proposed a new iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary and non-Gaussian processes. The proposed algorithm is rooted in the concept of defining the stochastic processes in the transform domain, which is elaborated and extend. The algorithm extends the iterative amplitude adjusted Fourier transform algorithm for generating surrogate and the spectral correction algorithm for simulating stationary non-Gaussian process. The IPAC algorithm can be used with different popular transforms, such as the Fourier transform, S-transform, and continuous wavelet transforms. The targets for the simulation are the marginal probability distribution function of the process and the power spectral density function of the process that is defined based on the variables in the transform domain for the adopted transform. The algorithm is versatile and efficient. Its application is illustrated using several numerical examples.

Multiscale Terrain Characterization Using Fourier and Wavelet Transforms for Unmanned Ground Vehicles

2009 ◽  
Author(s):  
Jeremy J. Dawkins ◽  
David M. Bevly ◽  
Robert L. Jackson
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Ground Vehicles ◽  
Quarter Car Model ◽  
Power Spectral ◽  
Before And After ◽  
Frequency Components ◽  
The Fourier Transform ◽  
Density Methods

This paper investigates the use of the Fourier transform and Wavelet transform as methods to supplement the more common root mean squared elevation and power spectral density methods of terrain characterization. Two dimensional terrain profiles were generated using the Weierstrass-Mandelbrot fractal equation. The Fourier and Wavelet transforms were used to decompose these terrains into a parameter set. A two degree of freedom quarter car model was used to evaluate the vehicle response before and after the terrain characterization. It was determined that the Fourier transform can be used to reduce the profile into the key frequency components. The Wavelet transform can effectively detect discontinuities of the profile and changes in the roughness of the profile. These two techniques can be added to current methods to yield a more robust terrain characterization.

scholarly journals Design and construction of a prototype for the analysis of vibrations in an induction motor for the detection of faults

2020 ◽  
pp. 27-33
Author(s):  
Javier Garrido ◽  
Beatris Escobedo-Trujillo ◽  
Guillermo Miguel Martínez-Rodríguez ◽  
Oscar Fernando Silva-Aguilar
Keyword(s):  
Fourier Transform ◽  
Induction Motor ◽  
Wavelet Transforms ◽  
Data Acquisition System ◽  
Time Frequency ◽  
Different Types ◽  
Control Devices ◽  
The Fourier Transform ◽  
And Control ◽  
Types Of Faults

The contribution of this work is to present the design of a prototype integrated by an induction motor, a data acquisition system, accelerometers and control devices for stop and start, to generate and identify different types of faults by means of vibration analysis. in the domain: time, frequency or frequency-time, through the use of the Fourier Transform, Fast Fourier Transform or Wavelet Transforms (wavelet transform). In this prototype, failures can be generated in the induction motor such as: unbalance, different types of misalignment, mechanical looseness, and electrical failures such as broken bars or short-circuited rings, an example of a misalignment failure is presented to show the process of analysis and detection.

scholarly journals ESTIMASI KETEBALAN SEDIMEN DENGAN ANALISIS POWER SPECTRAL PADA DATA ANOMALI GAYABERAT

GEOMATIKA ◽  
2018 ◽  
Vol 23 (2) ◽  
pp. 65 ◽  
Author(s):  
Mila Apriani ◽  
Admiral Musa Julius ◽  
Mahmud Yusuf ◽  
Damianus Tri Heryanto ◽  
Agus Marsono
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Gravity Anomaly ◽  
Spectral Method ◽  
Gravity Data ◽  
Sediment Thickness ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Power Spectral ◽  
The Fourier Transform

<p align="center"><strong>ABSTRAK</strong></p><p> </p><p>Penelitian dengan analisis <em>power spectral</em> data anomali gayaberat telah banyak dilakukan untuk estimasi ketebalan sedimen. Dalam studi ini penulis melakukan analisis spektral data anomali gayaberat wilayah DKI Jakarta untuk mengetahui kedalaman sumber anomali yang bersesuaian dengan ketebalan sedimen. Data yang digunakan berupa data gayaberat dari BMKG tahun 2014 dengan 197 lokasi titik pengukuran yang tersebar di koordinat 6,08º-6,36º LU dan 106,68º-106,97º BT. Studi ini menggunakan metode <em>power spectral</em>  dengan mentransformasikan data dari domain jarak ke dalam domain bilangan gelombang memanfaatkan transformasi <em>Fourier</em>. Hasil penelitian dengan menggunakan metode transformasi <em>Fourier  </em>menunjukkan bahwa ketebalan sedimen di Jakarta dari arah selatan ke utara semakin besar, di sekitar Babakan ketebalan diperkirakan 92 meter, sekitar Tongkol, Jakarta Utara diperkirakan 331 meter.</p><p><strong> </strong></p><p><strong>Kata kunci</strong>: <em>power spectral</em>, anomali gayaberat, ketebalan sedimen</p><p align="center"><strong><em> </em></strong></p><p align="center"><strong><em>ABSTRACT</em></strong></p><p><em> </em></p><p><em>Studies of spectral analysis of gravity anomaly data have been carried out to estimate the thickness of sediment. In this study the author did spectral analysis of gravity anomaly data of DKI Jakarta area to know the depth of anomaly source which corresponds to the thickness of sediment. The data used in the form of gravity data from BMKG 2014 with 197 locations of measurement points spread in coordinates 6.08º - 6.36º N and 106.68º - 106.97º E. This study used the power spectral method by transforming the data from the distance domain into the wavenumber domain utilizing the Fourier transform. The result of the research using Fourier transform method shows that the thickness of sediment in Jakarta from south to north is getting bigger, in Babakan the thickness of the sediment is around 92 meter, in Tongkol, North Jakarta is around 331 meter.</em></p><p><strong><em> </em></strong></p><p><strong><em>Keywords</em></strong><em>: </em><em>power spectral, gravity anomaly, sediment thickness</em><em></em></p>

scholarly journals Time-series Imputation Algorithm

2021 ◽  
Author(s):  
David Howe
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Time Series Data ◽  
Series Data ◽  
Allan Deviation ◽  
Original Time Series ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
The Fourier Transform ◽  
Original Time

Statistical imputation is a field of study that attempts to fill missing data. It is commonly applied to population statistics whose data have no correlation with running time. For a time series, data is typically analyzed using the autocorrelation function (ACF), the Fourier transform to estimate power spectral densities (PSD), the Allan deviation (ADEV), trend extensions, and basically any analysis that depends on uniform time indexes. We explain the rationale for an imputation algorithm that fills gaps in a time series by applying a backward, inverted replica of adjacent live data. To illustrate, four intentional massive gaps that exceed 100% of the original time series are recovered. The L(f) PSD with imputation applied to the gaps is nearly indistinguishable from the original. Also, the confidence of ADEV with imputation falls within 90% of the original ADEV with mixtures of power-law noises. The algorithm in Python is included for those wishing to try it.

A Spectral Representation Model for Simulation of Multivariate Random Processes

2011 ◽  
Vol 368-373 ◽  
pp. 1253-1258
Author(s):  
Jun Jie Luo ◽  
Cheng Su ◽  
Da Jian Han
Keyword(s):  
Spectral Density ◽  
Stochastic Processes ◽  
Power Spectral Density ◽  
Spectral Representation ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Recursive Algorithm ◽  
Spectral Density Function ◽  
Cholesky Factorization ◽  
Power Spectral

A model is proposed to simulate multivariate weakly stationary Gaussian stochastic processes based on the spectral representation theorem. In this model, the amplitude, phase angle, and frequency involved in the harmonic function are random so that the generated samples are real stochastic processes. Three algorithms are then adopted to improve the simulation efficiency. A uniform cubic B-spline interpolation method is employed to fit the target factorized power spectral density function curves. A recursive algorithm for the Cholesky factorization is utilized to decompose the cross-power spectral density matrices. Some redundant cosine terms are cut off to decrease the computation quantity of superposition. Finally, an example involving simulation of turbulent wind velocity fluctuations is given to validate the capability and accuracy of the proposed model as well as the efficiency of the optimal algorithms.

Stable reduction to the pole at the magnetic equator

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 571-578 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Fourier Transform ◽  
Magnetic Equator ◽  
Magnetic Data ◽  
Good Representation ◽  
Wavenumber Domain ◽  
Power Spectral ◽  
Reduction To The Pole ◽  
The Fourier Transform ◽  
Stable Reconstruction ◽  
Estimated Error

The solution of reduction to the pole (RTP) of magnetic data in the wavenumber domain faces a long standing difficulty of instability when the observed data are acquired at low magnetic latitudes or at the equator. We develop a solution to this problem that allows stable reconstruction of the RTP field with a high fidelity even at the magnetic equator. The solution is obtained by inverting the Fourier transform of the observed magnetic data in the wavenumber domain with explicit regularization. The degree of regularization is chosen according to the estimated error level in the data. The Fourier transform of the RTP field is constructed as a model that is maximally smooth and, at the same time, has a power‐spectral decay common to all fields produced by the same source. The applied regularization alleviates the singularity associated with the wavenumber‐domain RTP operator, and the imposed power spectral decay ensures that the constructed RTP field has the correct spectral content. As a result, the algorithm can perform the reduction to the pole stably at any magnetic latitude, and the constructed RTP field yields a good representation of the true field at the pole even when the reduction is carried out at the equator.

A SIGNAL-TUNED GABOR TRANSFORM WITH APPLICATION TO EEG ANALYSIS

2013 ◽  
Vol 24 (04) ◽  
pp. 1350017 ◽  
Author(s):  
JOSÉ R. A. TORREÃO ◽  
SILVIA M. C. VICTER ◽  
JOÃO L. FERNANDES
Keyword(s):  
Experimental Study ◽  
Fourier Transform ◽  
Input Signal ◽  
Fourier Component ◽  
Gabor Transform ◽  
Eeg Analysis ◽  
Time Frequency ◽  
Frequency Representation ◽  
S Transform ◽  
The Fourier Transform

We introduce a time-frequency transform based on Gabor functions whose parameters are given by the Fourier transform of the analyzed signal. At any given frequency, the width and the phase of the Gabor function are obtained, respectively, from the magnitude and the phase of the signal's corresponding Fourier component, yielding an analyzing kernel which is a representation of the signal's content at that particular frequency. The resulting Gabor transform tunes itself to the input signal, allowing the accurate detection of time and frequency events, even in situations where the traditional Gabor and S-transform approaches tend to fail. This is the case, for instance, when considering the time-frequency representation of electroencephalogram traces (EEG) of epileptic subjects, as illustrated by the experimental study presented here.

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