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Journal articles on the topic 'Fourier transformations'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

Azooz, A. "Experimentation with Fourier Transformations." International Journal of Electrical Engineering & Education 49, no. 2 (April 2012): 179–96. http://dx.doi.org/10.7227/ijeee.49.2.8.

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2

Treyderowski, Krzysztof, and Christoph Schwarzweller. "Multiplication of Polynomials using Discrete Fourier Transformation." Formalized Mathematics 14, no. 4 (January 1, 2006): 121–28. http://dx.doi.org/10.2478/v10037-006-0015-y.

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Multiplication of Polynomials using Discrete Fourier Transformation In this article we define the Discrete Fourier Transformation for univariate polynomials and show that multiplication of polynomials can be carried out by two Fourier Transformations with a vector multiplication in-between. Our proof follows the standard one found in the literature and uses Vandermonde matrices, see e.g. [27].

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3

Zolesio, Jean-Luc. "Transformations de Fourier discrètes: algorithmes rapides." Annales des Télécommunications 40, no. 9-10 (September 1985): 495–507. http://dx.doi.org/10.1007/bf02998222.

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4

Abe, Sumiyoshi, and John T. Sheridan. "Almost-Fourier and almost-Fresnel transformations." Optics Communications 113, no. 4-6 (January 1995): 385–88. http://dx.doi.org/10.1016/0030-4018(94)00521-u.

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5

Sadek, Bassel A., Elliot W. Martin, and Susan A. Shaheen. "Forecasting Truck Parking Using Fourier Transformations." Journal of Transportation Engineering, Part A: Systems 146, no. 8 (August 2020): 05020006. http://dx.doi.org/10.1061/jtepbs.0000397.

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6

Ginzburg, V. A. "Fourier?langlands transformations on reductive groups." Functional Analysis and Its Applications 22, no. 2 (1988): 143–44. http://dx.doi.org/10.1007/bf01077610.

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7

Ernst, Richard R. "Kernresonanz-Fourier-Transformations-Spektroskopie (Nobel-Vortrag)." Angewandte Chemie 104, no. 7 (July 1992): 817–36. http://dx.doi.org/10.1002/ange.19921040704.

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8

Azhar, Aurizan Himmi, Sugiyanto Sugiyanto, Muhammad Wakhid Musthofa, and Muhamad Zaki Riyanto. "Transformasi Fourier Multiplikatif Dan Aplikasinya Pada Persamaan Diferensial Multiplikatif." Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika 8, no. 2 (December 20, 2021): 149–60. http://dx.doi.org/10.31316/j.derivat.v8i2.1996.

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This research is a development of multiplicative calculus. This study is about the Fourier multiplicative transformation and its application to the multiplicative differential equation. This study aims to determine the Fourier multiplicative transformation as well as the multiplicative differential equation. This study contains numerical simulations to solve the problem of ordinary multiplicative differential equations of the first order. The methods used in this research are descriptive research methods through the study of literature. The results of this study are the application of multipli

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9

Parfentyev, Nikolay, Schubert Maignan, and Irina Tkachenko. "Delta function of the Fourier transform." E3S Web of Conferences 535 (2024): 01006. http://dx.doi.org/10.1051/e3sconf/202453501006.

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In the analysis of the double window Fourier transform, it is found that both components of the direct transformation contain an equal amount of information sufficient to restore the original time signal. A double conversion diagram has been constructed. For any initial signal, there is a conjugate signal having the same frequency spectrum. Analysis of the harmonic signal transformation showed that at an arbitrary phase of the harmonic, the frequency representation contains two functions: conditionally unipolar with a maximum at the initial frequency and bipolar with a zero value at the specif

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10

Langenbruch, Michael. "Asymptotic Fourier and Laplace transformations for hyperfunctions." Studia Mathematica 205, no. 1 (2011): 41–69. http://dx.doi.org/10.4064/sm205-1-4.

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11

Blank, R. "Holographic lenses for performing complete Fourier transformations." Optical Engineering 31, no. 3 (1992): 544. http://dx.doi.org/10.1117/12.56093.

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12

Younis, M. S. "Fourier transformations of functions with symmetrical differences." Acta Mathematica Hungarica 51, no. 3-4 (September 1988): 293–99. http://dx.doi.org/10.1007/bf01903336.

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13

Grabow, Jens-Uwe. "Fourier-Transformations-Mikrowellenspektroskopie: Händigkeit durch Rotationskohärenz gefasst." Angewandte Chemie 125, no. 45 (October 2, 2013): 11914–16. http://dx.doi.org/10.1002/ange.201307159.

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14

Fu, Lei. "Calculation of ℓ-adic local Fourier transformations". manuscripta mathematica 133, № 3-4 (1 липня 2010): 409–64. http://dx.doi.org/10.1007/s00229-010-0377-x.

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15

Ciulla, Carlo. "Theory and Applications of Fourier, Laplace, and Z Transformations." Journal of CIEES 2, no. 1 (July 26, 2022): 32–43. http://dx.doi.org/10.48149/jciees.2022.2.1.6.

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This study presents the mathematics for the implementation of direct and inverse Fourier, Laplace, and Z transformations. This research is at the intersection between signal processing, applied mathematics, and software engineering, and it provides a study guide to implementers. Mathematical concepts and details necessary to transform the math into code are provided as theoretical background. Validation is conducted for the cases when the transforms do intersect, when the transforms do not intersect, and when, in Fourier and Z-transformations, the frequency domain encodes a phase shift which i

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16

Pavlov V., Andrey. "The Fourier, Laplace Transformations and the Newton Potential." American Journal of Applied Mathematics and Statistics 2, no. 6 (November 5, 2014): 398–401. http://dx.doi.org/10.12691/ajams-2-6-7.

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17

Haider, Q., and L. C. Liu. "Fourier or Bessel transformations of highly oscillatory functions." Journal of Physics A: Mathematical and General 25, no. 24 (December 21, 1992): 6755–60. http://dx.doi.org/10.1088/0305-4470/25/24/026.

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18

Rezaee, S., M. Mohammadpour, and A. R. Soltani. "Stationary Processes via Fourier Transformations: Representation and Estimation." Iranian Journal of Science and Technology, Transactions A: Science 43, no. 3 (June 21, 2018): 937–45. http://dx.doi.org/10.1007/s40995-018-0590-0.

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19

Zotov, A. "Relativistic elliptic matrix tops and finite Fourier transformations." Modern Physics Letters A 32, no. 32 (October 12, 2017): 1750169. http://dx.doi.org/10.1142/s0217732317501693.

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We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter [Formula: see text]. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and [Fo

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20

Hudson, R. L. "On Hausdorff-Young inequalities for quantum fourier transformations." Ukrainian Mathematical Journal 49, no. 3 (March 1997): 514–22. http://dx.doi.org/10.1007/bf02487247.

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21

Fan, Hong-Yi, and Jun-Hua Chen. "On the core of the fractional Fourier transform and its role in composing complex fractional Fourier transformations and Fresnel transformations." Frontiers of Physics 10, no. 1 (February 2015): 1–6. http://dx.doi.org/10.1007/s11467-014-0445-x.

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22

Salamat, Kaushef, and Nousheen Ilyas. "DUALITIES BETWEEN FOURIER SINE AND SOME USEFUL INTEGRAL TRANSFORMATIONS." Journal of Mathematical Sciences & Computational Mathematics 2, no. 4 (July 5, 2021): 542–63. http://dx.doi.org/10.15864/jmscm.2408.

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The most useful technique of the mathematics which are used to finding the solutions of a lot of problems just like bending of beam, electrical network, heat related problems, which occurs in many disciplines of engineering and sciences are the techniques of integral transforms. In our research I discussed the duality between Fourier Sine transforms and some others effective integral transforms (namely Laplace transform, Mahgoub transform, Aboodh transform and Mohand transform). To justify the scope of dualities relation between Fourier Sine transform and other integral transforms (that are me

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23

Hu, Liang‐Zie, and George A. McMechan. "Wave‐field transformations of vertical seismic profiles." GEOPHYSICS 52, no. 3 (March 1987): 307–21. http://dx.doi.org/10.1190/1.1442305.

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Vertical seismic profile (VSP) data may be partitioned in a variety of ways by application of wave‐field transformations. These transformations provide insights into the nature of the data and aid in the design of processing operations. Transformations are implemented in a reversible sequence that takes the observed VSP data from the depth‐time (z-t) domain through the slowness‐time intercept (p-τ) domain (by a slant stack), to the slowness‐frequency (p-ω) domain (by a 1-D Fourier transform over τ), to the wavenumber‐frequency (k-ω) domain (by resampling using the Fourier central‐slice theorem

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24

Sharyn, S. V. "Algebraic and differential properties of polynomial Fourier transformation." Matematychni Studii 53, no. 1 (March 17, 2020): 59–68. http://dx.doi.org/10.30970/ms.53.1.59-68.

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Methods of integral transformations of (generalized) functions are widely used in the solution of initial and boundary value problems for partial differential equations. However, many problems in applied mathematics require a nonlinear generalization of distribution spaces. Besides, an algebraic structure of a space of distributions is desirable, which is needed, for example, in quantum field theory.In the article, we use the adjoint operator method as well as technique of symmetric tensor products to extended the Fourier transformation onto the spaces of so-called polynomial rapidly decreasin

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25

AGHILI, S. ALIREZA, DIVYAKANT AGRAWAL, and AMR EL ABBADI. "SEQUENCE SIMILARITY SEARCH USING DISCRETE FOURIER AND WAVELET TRANSFORMATION TECHNIQUES." International Journal on Artificial Intelligence Tools 14, no. 05 (October 2005): 733–54. http://dx.doi.org/10.1142/s0218213005002363.

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In this paper, we study the problem of sequence similarity search. We incorporate vector transformations and apply DFT (Discrete Fourier Transformation) and DWT (Discrete Wavelet Transformation, Haar) dimensionality reduction techniques to reduce the search space/time of sequence similarity range queries. Our empirical results on a number of Prokaryote and Eukaryote DNA contig databases demonstrate up to 50-fold filtration ratio reduction of the search space and up to 13 times faster filtration. The proposed transformation techniques may easily be integrated as a pre-processing phase on top of

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26

Critchley-Marrows, Joshua, Samanvay Karambhe, Denzil Khan, Elias Vasilikas, and Gareth A. Vio. "Identification of Nonlinearities Using Computational Approaches." Applied Mechanics and Materials 846 (July 2016): 559–64. http://dx.doi.org/10.4028/www.scientific.net/amm.846.559.

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This paper presents an analysis into the computational results for modelling of a two degree-of-freedom nonlinear vibrating structure. Fast Fourier Transformations, Short Time Fourier Transformations, Hilbert Transformations and wavelets are used to model this system. These techniques aim to locate and quantify the nonlinear behaviour of the system. Coulomb friction was detected with a number of these techniques, however other nonlinearities could not be detected. From the analysis conducted, improved computational methods are necessary for the detection of nonlinearities.

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27

Sobchuk, Valentin, and Galina Kharkevych. "DEPENDENCE OF THE QUALITY OF MACHINE TRANSLATION OF THE TEXT ON THE USED FOURIER TRANSFORMATION." Journal of Automation and Information sciences 4 (July 1, 2021): 69–80. http://dx.doi.org/10.34229/1028-0979-2021-4-7.

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Machine translation is widely used in the translation of commercial, technical, scientific information that is connected with the process of globalization and, accordingly, the expansion of the network of business relations. Mathematical methods related to machine translation of the texts have recently received new development due to the intensive development of Fourier transformation theory. Thus, the requirements for filtering accuracy in the processing of contrast signals and images have increased, allowing to create efficient filtering algorithms. Frequency algorithms are the most efficien

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28

Polovynko, Ihor, and Lubomyr Kniazevich. "Improvement of images by using graduate transformations of their Fourier depictions." Technology audit and production reserves 2, no. 2(58) (April 30, 2021): 16–19. http://dx.doi.org/10.15587/2706-5448.2021.230079.

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The object of research is low-quality digital images. The presented work is devoted to the problem of digital processing of low quality images, which is one of the most important tasks of data science in the field of extracting useful information from a large data set. It is proposed to carry out the process of image enhancement by means of tonal processing of their Fourier images. The basis for this approach is the fact that Fourier images are described by brightness values in a wide range of values, which can be significantly reduced by gradation transformations. The work carried out the Fou

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29

Gafiyatov, R. N. "Acoustic waves in two-fraction mixtures of liquid with vapor-gas bubbles." Proceedings of the Mavlyutov Institute of Mechanics 9, no. 1 (2012): 65–68. http://dx.doi.org/10.21662/uim2012.1.011.

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The mathematical model of two-fractional mixture of liquid with vapor-gas bubbles of different gases and sizes with phase transformations is presented. The dispersive equation is received, dispersive curves that determine the propagation of acoustic disturbances was plotted. Calculations on the propagation of impulse pressure perturbations were performed by means of a fast Fourier transformation method.

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30

He, Y., K. Hueske, J. Götze, and E. Coersmeier. "Matrix-Vector Based Fast Fourier Transformations on SDR Architectures." Advances in Radio Science 6 (May 26, 2008): 89–94. http://dx.doi.org/10.5194/ars-6-89-2008.

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Abstract. Today Discrete Fourier Transforms (DFTs) are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex). It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT) engines. However, in face of the Software Defined Radio (SDR) development, more general (parallel) processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based descr

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31

Azana, J., and M. A. Muriel. "Real-time Fourier transformations performed simultaneously over multiwavelength signals." IEEE Photonics Technology Letters 13, no. 1 (January 2001): 55–57. http://dx.doi.org/10.1109/68.903219.

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32

Goginava, Ushangi, Sawsan Omira, Reem Abdel-Latif, and Tasnem AlKrinat. "Matrix transformations of sequences and applications in Fourier analysis." Heliyon 10, no. 8 (April 2024): e29585. http://dx.doi.org/10.1016/j.heliyon.2024.e29585.

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33

Dubrovkin, Joseph. "Linear transformations of multivariate calibration models in near infrared spectroscopy: A comparative study." Journal of Near Infrared Spectroscopy 25, no. 4 (July 30, 2017): 223–30. http://dx.doi.org/10.1177/0967033517723253.

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It was shown that linear transformations are suitable for use in multivariate calibration in near infrared spectroscopy as data compression tools. Partial Least Squares calibration models were built using spectral data transformed by expansion in the series of classical orthogonal polynomials, Fourier and wavelet harmonics. These models allowed effective prediction of the cetane number of diesel fuels, Brix and pol parameters of syrup in sugar production and fat and total protein content in milk. Depending on the compression ratio, prediction errors were no larger than 30% of corresponding err

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34

NILL, FLORIAN. "WEYL ALGEBRAS, FOURIER TRANSFORMATIONS AND INTEGRALS ON FINITE-DIMENSIONAL HOPF ALGEBRAS." Reviews in Mathematical Physics 06, no. 01 (February 1994): 149–66. http://dx.doi.org/10.1142/s0129055x94000092.

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The "Weyl algebras" [Formula: see text], σ, σ′ ∈ {+, –}, over a finite-dimensional Hopf algebra H are defined to be the abstract algebras generated by left or right (σ = ±) multiplication operators Qσ (ψ), ψ ∈ H, and left or right (σ′ = ±) translation operators Pσ′ (a), [Formula: see text] dual of H. It is shown that these algebras are all isomorphic to End (H). Fourier transformations are defined as intertwiners [Formula: see text] implementing a natural isomorphism [Formula: see text]. As a byproduct, this formalism provides a new proof of the invertibility of the antipode and the uniqueness

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35

Slobodianuk, Olena. "Abstract law and actual reality: social critique from F. Poullain de la Barre to Charles Fourier." Sententiae 5, no. 1 (April 22, 2002): 130–43. http://dx.doi.org/10.31649/sent05.01.130.

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The article compares the views of François Poullain de la Barre and Charles Fourier on gender equality. The research is based on the background of historical and philosophical transformations associated with the transition from Cartesian rationalism to enlightenment and post-enlightenment thinking. The latter focuses primarily on social criticism and human transformation through the transformation of social relations. Although the author states that some of the provisions of French philosophers have a common origin (the ideological potential of Cartesianism and the modern doctrine of natural l

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36

Tao, Ngo Quoc. "Extracting invariants based on coordinate transformations." Journal of Computer Science and Cybernetics 9, no. 4 (April 26, 2016): 28–32. http://dx.doi.org/10.15625/1813-9663/9/4/8255.

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This paper deals with some methods extracting invariants for the translation, rotation and scaling and finding invariants which are depended on statistic invariants. It collates them with the Fourier transform. For discrete point set we can use the polar coordinate to construct SCC (star contour code) and give match algorithm for SCC.

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37

Balsa, Jose. "Comparison of Image Compressions: Analog Transformations." Proceedings 54, no. 1 (August 21, 2020): 37. http://dx.doi.org/10.3390/proceedings2020054037.

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A comparison between the four most used transforms, the discrete Fourier transform (DFT), discrete cosine transform (DCT), the Walsh–Hadamard transform (WHT) and the Haar-wavelet transform (DWT), for the transmission of analog images, varying their compression and comparing their quality, is presented. Additionally, performance tests are done for different levels of white Gaussian additive noise.

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38

Zhao, Tieyu, and Yingying Chi. "Quantum Weighted Fractional-Order Transform." Fractal and Fractional 7, no. 3 (March 18, 2023): 269. http://dx.doi.org/10.3390/fractalfract7030269.

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Quantum Fourier transform (QFT) transformation plays a very important role in the design of many quantum algorithms. Fractional Fourier transform (FRFT), as an extension of the Fourier transform, is particularly important due to the design of its quantum algorithm. In this paper, a new reformulation of the weighted fractional Fourier transform (WFRFT) is proposed in order to realize quantum FRFT; however, we found that this reformulation can be applied to other transformations, and therefore, this paper presents the weighted fractional Hartley transform (WFRHT). For the universality of applica

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39

Küchenmeister, Jens. "Three-dimensional adaptive coordinate transformations for the Fourier modal method." Optics Express 22, no. 2 (January 14, 2014): 1342. http://dx.doi.org/10.1364/oe.22.001342.

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40

Penmetsa, Ravi C., and Ramana V. Grandhi. "Adaptation of fast Fourier transformations to estimate structural failure probability." Finite Elements in Analysis and Design 39, no. 5-6 (March 2003): 473–85. http://dx.doi.org/10.1016/s0168-874x(02)00104-x.

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41

Pfirsch, Frank, and Michael C. Böhm. "On the accuracy of fourier transformations in crystal orbitat approaches." Chemical Physics 98, no. 1 (August 1985): 89–98. http://dx.doi.org/10.1016/0301-0104(85)80097-5.

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42

Gogolewski, Damian, Paweł Zmarzły, Tomasz Kozior, and Thomas G. Mathia. "Possibilities of a Hybrid Method for a Time-Scale-Frequency Analysis in the Aspect of Identifying Surface Topography Irregularities." Materials 16, no. 3 (January 31, 2023): 1228. http://dx.doi.org/10.3390/ma16031228.

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The article presents research results related to assessing the possibilities of applying modern filtration methods to diagnosing measurement signals. The Fourier transformation does not always provide full information about the signal. It is, therefore, appropriate to complement the methodology with a modern multiscale method: the wavelet transformation. A hybrid combination of two algorithms results in revealing additional signal components, which are invisible in the spectrum in the case of using only the harmonic analysis. The tests performed using both simulated signals and the measured ro

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43

Chakraborty, Avijit, and David Okaya. "Frequency‐time decomposition of seismic data using wavelet‐based methods." GEOPHYSICS 60, no. 6 (November 1995): 1906–16. http://dx.doi.org/10.1190/1.1443922.

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Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency‐time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time‐ frequency resolution limitation. Recently developed transforms based on

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44

Gitin, Andrey V. "Mathematical Fundamentals of Modern Linear Optics." International Journal of Antennas and Propagation 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/273107.

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All known quantum-mechanical approaches to wave and statistical optics are united into a single theory, using Feynman's path integral as a fundamental principle. In short-wave approximations, this principle, the Fourier transformations, and concepts of the theory reproduce Fermat's principle, the Legendre transformations, and concepts of Hamilton's optics and radiometry in a one-to-one fashion.

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45

Merakos, P. K., K. Masselos, and C. E. Goutis. "Power Efficient Hierarchical Scheduling for DSP Transformations." VLSI Design 14, no. 2 (January 1, 2002): 203–17. http://dx.doi.org/10.1080/10655140290010114.

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In this paper, the problem of scheduling the computation of partial products in transformational Digital Signal Processing (DSP) algorithms, aiming at the minimization of the switching activity in data and address buses, is addressed. The problem is stated as a hierarchical scheduling problem. Two different optimization algorithms, which are based on the Travelling Salesman Problem (TSP), are defined. The proposed optimization algorithms are independent on the target architecture and can be adapted to take into account it. Experimental results obtained from the application of the proposed algo

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46

Morimoto, Mitsuo, and Keiko Fujita. "Conical Fourier-Borel transformations for harmonic functionals on the Lie ball." Banach Center Publications 37, no. 1 (1996): 95–113. http://dx.doi.org/10.4064/-37-1-95-113.

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47

Vetterli, Martin, and Henri J. Nussbaumer. "Algorithmes de transformations de Fourier et en cosinus mono et bidimensionnels." Annales des Télécommunications 40, no. 9-10 (September 1985): 466–76. http://dx.doi.org/10.1007/bf02998219.

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48

Wada, Ryoko. "The Fourier-Borel transformations of analytic functionals on the complex sphere." Proceedings of the Japan Academy, Series A, Mathematical Sciences 61, no. 9 (1985): 298–301. http://dx.doi.org/10.3792/pjaa.61.298.

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49

Agafonova, N. Yu. "On Uniform Convergence of Transformations of Fourier Series on Multiplicative Systems." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 9, no. 1 (2009): 3–8. http://dx.doi.org/10.18500/1816-9791-2009-9-1-3-8.

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50

VanderLugt, A., C. S. Anderson, and P. J. W. Melsa. "Time-delay detection of short pulses by Fresnel and Fourier transformations." Applied Optics 32, no. 20 (July 10, 1993): 3761. http://dx.doi.org/10.1364/ao.32.003761.

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