scholarly journals Invariants of optimal integration of rapidly oscillatory functions

2021 ◽  
pp. 121-125
Author(s):  
Valeriy Zadiraka ◽  
Liliya Luts ◽  
Inna Shvidchenko
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Computer Technology ◽  
Quadrature Formulas ◽  
Common Elements ◽  
Optimal Integration ◽  
Different Types ◽  
Bessel Transform ◽  
The Fourier Transform ◽  
Computational Resources

The paper presents some common elements (invariants) of optimal integration of rapidly oscillatory functions for the different types of oscillations, in particular, for calculating the Fourier transform from finite functions, wavelet transform, and Bessel transform. Their brief description is given. The application of the invariants allows to increase the potential of quadrature formulas due to the fullest use of apriori information. Invariants form the basis of computer technology of integration of rapidly oscillatory functions with a given accuracy with limited computational resources.

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 Extracting Features of Transient Electric Fields With Fourier And Wavelet Transform–A Case Study Of Lightning Positive Return Stroke

2021 ◽  
Vol 14 (14) ◽  
pp. 44-50
Author(s):  
Shriram Sharma
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Spectral Density ◽  
Frequency Spectrum ◽  
Electric Fields ◽  
Frequency Range ◽  
Return Stroke ◽  
The Fourier Transform ◽  
Positive Return ◽  
Domain Information

Frequency domain information were extracted from the time domain electric fields pertinent to the lightning positive return strokes applying Fourier transform and Wavelet transform. The electric field radiated by positive ground flashes striking the sea were recorded at 10 ns resolution at a coastal station to minimize the propagation effects. The frequency spectrum of the electric field of positive return strokes were computed applying the Fourier transform technique in the range of 10 kHz to 20 MHz owing to the fact that this range of frequency is of very much interest to the researchers and design engineers. The amplitude of the energy spectral density decreases nearly as ƒ-1 from 10 kHz to about 0.1 MHz and drops nearly as ƒ-2 up to 8 MHz.  Applying the wavelet transform technique, the same positive return strokes are found to radiate in the frequency range of 5.5 to 81 kHz with the average spread distribution of 13.6 kHz to about 30 kHz. From frequency spectrum obtained from the Fourier transform it is difficult to identify as which phase of the return stroke radiates in the higher frequency range and that in the lower frequency range, whereas, one can easily identify from the frequency spectrum obtained with the wavelet transform that ramp portion of the positive return stroke radiates in the larger spectral range as compared to that of initial peak of the return stroke.  Also, from the spectral density map obtained from wavelet transform one can easily observe the contribution of each phase in a range of frequency, which is not possible from the Fourier transform technique. Clearly, the wavelet transform is much more powerful tool to extract the frequency domain information of a non-stationary signal as compared to that of Fourier transform.

scholarly journals Another approach to the evaluation of a certain multivariate compound distribution

2016 ◽  
Vol 24 (3) ◽  
pp. 339-349
Author(s):  
Elena-Gratiela Robe-Voinea ◽  
Raluca Vernic
Keyword(s):  
Fourier Transform ◽  
Probability Function ◽  
Probability Generating Function ◽  
Recursive Formula ◽  
Aggregate Model ◽  
Insurance Portfolio ◽  
Compound Distribution ◽  
Different Types ◽  
New Form ◽  
The Fourier Transform

AbstractIn this work, we consider the multivariate aggregate model introduced in [11], model that takes into account the case when different types of claims affect in the same time an insurance portfolio under some specific assumptions related to the number of claims. For the probability function of the corresponding multivariate compound distribution, [11] obtained an exact recursive formula proved using the properties of the probability generating function. In this paper, we present a new shorter proof of the same formula that we also extend to a new form. Moreover, we present an alternative approximate method to evaluate the compound distribution based on the Fourier transform, and we compare both methods on a numerical example.

CONTOUR-BASED FEATURE EXTRACTION USING DUAL-TREE COMPLEX WAVELETS

2007 ◽  
Vol 21 (07) ◽  
pp. 1233-1245 ◽  
Author(s):  
G. Y. CHEN ◽  
W. F. XIE
Keyword(s):  
Feature Extraction ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Invariant Property ◽  
Complex Wavelet Transform ◽  
Translation Invariant ◽  
Feature Extraction Method ◽  
Complete Representation ◽  
Complex Wavelet ◽  
The Fourier Transform

A contour-based feature extraction method is proposed by using the dual-tree complex wavelet transform and the Fourier transform. Features are extracted from the 1D signals r and θ, and hence the processing memory and time are reduced. The approximate shift-invariant property of the dual-tree complex wavelet transform and the Fourier transform guarantee that this method is invariant to translation, rotation and scaling. The method is used to recognize aircrafts from different rotation angles and scaling factors. Experimental results show that it achieves better recognition rates than that which uses only the Fourier features and Granlund's method. Its success is due to the desirable shift invariant property of the dual-tree complex wavelet transform, the translation invariant property of the Fourier spectrum, and our new complete representation of the outer contour of the pattern.

Research of the Seismic Wave Data Processing Based on the Wavelet Transform

2013 ◽  
Vol 273 ◽  
pp. 184-187
Author(s):  
De En ◽  
Na Na Wei ◽  
Huang He Wei ◽  
Xiao Long Shi ◽  
Chang Sheng Zhou
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Seismic Data ◽  
Underground Structure ◽  
Data Interpretation ◽  
Synthetic Seismogram ◽  
Seismic Exploration ◽  
In The Wild ◽  
Soft Threshold ◽  
The Fourier Transform

Seismic exploration is a effective methods to ascertain underground structure and looking for oil. As the data collected in the wild are often subjected to the interference of noise, is not conducive to the analysis and interpretation of seismic data, therefore removing noise is the premise of data interpretation. To use the Fourier transform and wavelet analysis denoising a synthetic seismogram in this paper, by comparing denoising results, wavelet soft threshold denoising waveform is smooth, and it can better reconstruction original waveform.

scholarly journals Time Frequency Analysis of Wavelet and Fourier Transform

2020 ◽  
Author(s):  
Karlton Wirsing
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Domain ◽  
Frequency Analysis ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Efficient Access ◽  
The Fourier Transform

Signal processing has long been dominated by the Fourier transform. However, there is an alternate transform that has gained popularity recently and that is the wavelet transform. The wavelet transform has a long history starting in 1910 when Alfred Haar created it as an alternative to the Fourier transform. In 1940 Norman Ricker created the first continuous wavelet and proposed the term wavelet. Work in the field has proceeded in fits and starts across many different disciplines, until the 1990’s when the discrete wavelet transform was developed by Ingrid Daubechies. While the Fourier transform creates a representation of the signal in the frequency domain, the wavelet transform creates a representation of the signal in both the time and frequency domain, thereby allowing efficient access of localized information about the signal.

scholarly journals Bond yields and stock returns comparison using wavelet semblance analysis

2017 ◽  
Vol 14 (2) ◽  
pp. 281-289 ◽  
Author(s):  
Robert Verner ◽  
Gabriel Herbrik
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Stock Returns ◽  
Continuous Wavelet Transform ◽  
Stock Prices ◽  
Continuous Wavelet ◽  
Government Bond ◽  
Bond Yields ◽  
The Fourier Transform ◽  
Different Sources

Various measures of resemblance are increasingly applied in confrontation of data samples obtained by different sources. Semblance analysis aims at comparison of two sets of data based on their phase and frequency. Conventional semblance analysis following the Fourier transform has several deficiencies resulting from the transform. To overcome these obstacles, another type of semblance analysis was developed applying the wavelet transform. This paper focuses on semblance analysis of stock prices and government bond yields of two major global economies using continuous wavelet transform regarding both scale and time.

Sign in / Sign up

Export Citation Format

Share Document