The Fourier transform and spectral analysis

2003 ◽  
pp. 247-283
Author(s):  
Bernard Mulgrew
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
The Fourier Transform

scholarly journals Spectral Analysis of Traffic Functions in Urban Areas

2015 ◽  
Vol 27 (6) ◽  
pp. 477-484 ◽  
Author(s):  
Florin Nemtanu ◽  
Ilona Madalina Costea ◽  
Catalin Dumitrescu
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Fourier Analysis ◽  
Traffic Flow ◽  
Traffic Control ◽  
Urban Areas ◽  
Urban Traffic ◽  
The Fourier Transform ◽  
The City ◽  
Different Time Scales

The paper is focused on the Fourier transform application in urban traffic analysis and the use of said transform in traffic decomposition. The traffic function is defined as traffic flow generated by different categories of traffic participants. A Fourier analysis was elaborated in terms of identifying the main traffic function components, called traffic sub-functions. This paper presents the results of the method being applied in a real case situation, that is, an intersection in the city of Bucharest where the effect of a bus line was analysed. The analysis was done using different time scales, while three different traffic functions were defined to demonstrate the theoretical effect of the proposed method of analysis. An extension of the method is proposed to be applied in urban areas, especially in the areas covered by predictive traffic control.

The Fourier transform and spectral analysis

1999 ◽  
pp. 240-277
Author(s):  
Bernard Mulgrew ◽  
Peter Grant ◽  
John Thompson
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
The Fourier Transform

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 How can the Fourier Transform be Used in Radio Astronomy to Perform Spectral Analysis of Pulsars

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Pranesh Kumar ◽  
Arthur Western
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Low Frequency ◽  
Radio Frequency Interference ◽  
Radio Waves ◽  
Folding Algorithm ◽  
Radio Signals ◽  
Multiple Characteristics ◽  
The Fourier Transform

The analysis of pulsars is a complicated procedure due to the influence of background radio waves. Special radio telescopes designed to detect pulsar signals have to employ many techniques to reconstruct interstellar signals and determine if they originated from a pulsating radio source. The Discrete Fourier Transform on its own has allowed astronomers to perform basic spectral analysis of potential pulsar signals. However, Radio Frequency Interference (RFI) makes the process of detecting and analyzing pulsars extremely difficult. This has forced astronomers to be creative in identifying and determining the specific characteristics of these unique rotating neutron stars. Astrophysicists have utilized algorithms such as the Fast Fourier Transform (FFT) to predict the spin period and harmonic frequencies of pulsars. However, FFT-based searches cannot be utilized alone because low-frequency pulsar signals go undetected in the presence of background radio noise. Astrophysicists must stack up pulses using the Fast Folding Algorithm (FFA) and utilize the coherent dedispersion technique to improve FFT sensitivity. The following research paper will discuss how the Discrete Fourier Transform is a useful technique for detecting radio signals and determining the pulsar frequency. It will also discuss how dedispersion and the pulsar frequency are critical for predicting multiple characteristics of pulsars and correcting the influence of the Interstellar Medium (ISM).

APPLICATION OF KOTELNIKOV’S THEOREM TO ANALYSIS OF RANDOM PROCESSES

2019 ◽  
pp. 28-34
Author(s):  
O. V. Goriunov ◽  
S. V. Slovtsov
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Random Process ◽  
Spectral Characteristics ◽  
Random Processes ◽  
Statistical Characteristics ◽  
Signal Spectrum ◽  
The Fourier Transform ◽  
The Stability ◽  
Correlation And Spectral Analysis

Analysis of many dynamic tasks arising in engineering applications is associated with the construction of spectral characteristics. However, the application of spectral analysis to random oscillations, which in most cases describe real processes (technical, technological, etc.), has a number of features and limitations associated, in particular, with the anconvergence of the Fourier transform. The substantiated metrological evaluation of the spectra associated with the reliability of the applied results is complicated by the absence of a rigorous mathematical model of a random process. The above remarks were solved on the basis of application of Kotelnikov's theorem at decomposition of a random process on known eigenfunctions. The obtained decomposition allowed us to obtain a number of results in the field of correlation and spectral analysis of random processes: the stability of the ACF and the relationship with the statistical characteristics of the implementation is proved, the orthogonal decomposition of the random process in the form of a continuous function is presented, which allows us to consider the evaluation and analyze the characteristics of the realizations without the use of a fast Fourier transform; the natural relationship between ACF and spectral density for a time-limited signal is shown, and the symmetric form of recording the signal spectrum is justified.

scholarly journals Rotor Fault Detection in Induction Motors Based on Time-Frequency Analysis Using the Bispectrum and the Autocovariance of Stray Flux Signals

Energies ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 597 ◽  
Author(s):  
Miguel Iglesias-Martínez ◽  
Jose Antonino-Daviu ◽  
Pedro Fernández de Córdoba ◽  
J. Conejero
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Induction Motor ◽  
Mean Value ◽  
High Order ◽  
One Dimensional ◽  
Time Frequency ◽  
Temporal Domain ◽  
The Fourier Transform ◽  
The One

The aim of this work is to find out, through the analysis of the time and frequency domains, significant differences that lead us to obtain one or several variables that may result in an indicator that allows diagnosing the condition of the rotor in an induction motor from the processing of the stray flux signals. For this, the calculation of two indicators is proposed: the first is based on the frequency domain and it relies on the calculation of the sum of the mean value of the bispectrum of the flux signal. The use of high order spectral analysis is justified in that with the one-dimensional analysis resulting from the Fourier Transform, there may not always be solid differences at the spectral level that enable us to distinguish between healthy and faulty conditions. Also, based on the high-order spectral analysis, differences may arise that, with the classical analysis with the Fourier Transform, are not evident, since the high order spectra from the Bispectrum are immune to Gaussian noise, but not the results that can be obtained using the one-dimensional Fourier transform. On the other hand, a second indicator based on the temporal domain that is based on the calculation of the square value of the median of the autocovariance function of the signal is evaluated. The obtained results are satisfactory and let us conclude the affirmative hypothesis of using flux signals for determining the condition of the rotor of an induction motor.

scholarly journals Standard and singular wavelet analysis

2021 ◽  
pp. 39-44
Author(s):  
V. M. Romanchak ◽  
M. A. Hundzina
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Wavelet Analysis ◽  
Applied Research ◽  
Main Tool ◽  
Point Of View ◽  
Periodic Signal ◽  
Periodic Signals ◽  
The Fourier Transform ◽  
Intuitive Interpretation

The paper suggests that the use of classical wavelets may be auxiliary in the analysis of a periodic signal. This is because the intuitive interpretation of the wavelet transform is not obvious. It is proposed to consider the Fourier transform as the main tool in applied research of periodic signals. An example is provided to support this point of view. To isolate the periodic component of the signal, along with wavelet analysis, it is proposed to perform spectral analysis. To do this, pre-filtering is performed using singular wavelets. This approach can significantly complement classical wavelet analysis.

scholarly journals A Guide on Spectral Methods Applied to Discrete Data in One Dimension

2017 ◽  
Vol 2017 ◽  
pp. 1-27 ◽  
Author(s):  
Martin Seilmayer ◽  
Matthias Ratajczak
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Spectral Methods ◽  
Discrete Data ◽  
Time Dependent ◽  
One Dimension ◽  
One Dimensional ◽  
The Common ◽  
The Fourier Transform ◽  
Fragmented Data

This paper provides an overview about the usage of the Fourier transform and its related methods and focuses on the subtleties to which the users must pay attention. Typical questions, which are often addressed to the data, will be discussed. Such a problem can be the origin of frequency or band limitation of the signal or the source of artifacts, when a Fourier transform is carried out. Another topic is the processing of fragmented data. Here, the Lomb-Scargle method will be explained with an illustrative example to deal with this special type of signal. Furthermore, the time-dependent spectral analysis, with which one can evaluate the point in time when a certain frequency appears in the signal, is of interest. The goal of this paper is to collect the important information about the common methods to give the reader a guide on how to use these for application on one-dimensional data. The introduced methods are supported by the spectral package, which has been published for the statistical environment R prior to this article.

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