Wyniki wyszukiwania - Biblioteka Nauki

1

Application of Hybrid Fourier Wavelet Transform to Data Space Reduction in Clothing Sales Volume Time Series

100%

Lipiński P. , Yatsymirskyy M.

Journal of Applied Computer Science

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2008

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tom Vol. 16, nr 1

81-88

EN

The main contribution of this article is the application of hybrid Fourier wavelet transform to data space reduction in clothing sales volume time series. We show that hybrid Fourier wavelet transform can be used to reduce the data space of abovementioned time series and gives promising results. The reduction of data space achieved using hybrid Fourier wavelet transform is advantageous when compared to Fourier and wavelet transforms.

2

A gradient-projective basis of compactly supported wavelets in dimension n > 1

100%

Battle G.

Open Mathematics

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2013

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tom 11

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nr 7

1317-1333

EN

A given set W = {W X } of n-variable class C 1 functions is a gradient-projective basis if for every tempered distribution f whose gradient is square-integrable, the sum $\sum\limits_\chi {(\int_{\mathbb{R}^n } {\nabla f \cdot } \nabla W_\chi ^* )} W_\chi $ converges to f with respect to the norm $\left\| {\nabla ( \cdot )} \right\|_{L^2 (\mathbb{R}^n )} $ . The set is not necessarily an orthonormal set; the orthonormal expansion formula is just an element of the convex set of valid expansions of the given function f over W. We construct a gradient-projective basis W = {W x } of compactly supported class C 2−ɛ functions on ℝn such that [...] where X has the structure $\chi = (\tilde \chi ,\nu )$ , ν ∈ ℤ. W is a wavelet set in the sense that the functions indexed by $\tilde \chi $ are generated by an averaging of lattice translations with wave propagations, and there are two additional discrete parameters associated with the latter. These functions indexed by $\tilde \chi $ are the unit-scale wavelets. The support volumes of our unit-scale wavelets are not uniformly bounded, however. While the practical value of this construction is doubtful, our motivation is theoretical. The point is that a gradient-orthonormal basis of compactly supported wavelets has never been constructed in dimension n > 1. (In one dimension the construction of such a basis is easy - just anti-differentiate the Haar functions.)

3

Holographic elements for Fourier transform

80%

Jagoszewski E. , Andruchów A.

Optica Applicata

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2004

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tom Vol. 34, nr 1

63-75

EN

Problems of designing the holographic Fourier transform elements are described. First, two different configurations for a Fourier transform setup are considered. The converging beam Fourier transform (CB-FT) is simpler than the conventional parallel beam Fourier transform (PB-FT) setup, and it appears that it should be preferred in ordinary cases. But the advantage of the conventional configuration is to make the Fourier plane free of the spherical factor. In order to obtain an exact Fourier transform, the design of holographic lens is described with respect to its optimization. A major problem is to eliminate possibly all aberrations, especially distortion for high values of spatial frequencies, threrefore we have shown the advantage of curved holographic element which could be applied to Fourier transform operation

4

An Image Authentication Based on Discrete Fourier Transform

80%

Kieu T. D. , Chang C.-C.

Fundamenta Informaticae

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2009

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tom Vol. 97, nr 4

369-379

EN

The advances of network technologies and digital devices facilitate users to exchange multimedia data over the public networks. However, this also raises significant concerns about how to protect sensitive multimedia data from being illegally copied and unauthorized modifications. Thus, this paper proposes a fragile watermarking method to detect illegitimate alterations of the watermarked data. The proposed method embeds a grayscale watermark image into a grayscale cover image in a block-by-block manner by using discrete Fourier transform. Experimental results show that the proposedmethod can successfully and exactly detect and localize any tampered regions of the watermarked image.

5

Pricing correlation options: from the P. Carr and D. Madan approach to the new method based on the Fourier transform

80%

Orzechowski A.

Economics and Business Review

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2018

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tom 4(18)

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nr 1

16-28

EN

Pricing of options plays an important role in the financial industry. Investors knowing how to price derivative contracts quickly and accurately can beat the market. On the other hand market participants constructing their investment strategies with the use of options based on techniques that do not assure the highest computational speed and efficiency are doomed to failure. The aim of the article is to extend the existing methodology of pricing correlation options based on the Fourier transform. The article starts with a presentation of Carr and Madan’s concept (Carr & Madan, 1999). Then other methods of pricing options with the use of the Fourier transform are summarized. Finally, a new approach to pricing derivative contracts is derived and then applied to the correlation options.

6

Experimental study of an anomalous hollow beam with orbital angular momentum

80%

Lu X. , Zhao C. , Hoenders B. J. , Yang Y. , Cai Y.

Optica Applicata

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2019

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tom Vol. 49, nr 2

217--226

EN

Anomalous hollow beam has potential applications in the optical trapping and free space optical communications, etc. It is noted that, thus far, although a large number of studies have been carried out in this field, most of them are theoretical studies and only quite a few cases have experimental results. Here, we experimentally study the generating of anomalous hollow beam carrying orbital angular momentum, and measure its topological charge. We show that the number of dark rings in the Fourier transform of intensity patterns is equal to the topological charge. The experimental results agree well with the simulations.

7

Sound Wave Radiation from Partially Lined Duct

80%

Tiryakioglu B. , Demir A.

Archives of Acoustics

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2019

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tom Vol. 44, No. 2

239--249

EN

The radiation of sound waves from partially lined duct is treated by using the mode-matching method in conjunction with the Wiener-Hopf technique. The solution is obtained by modification of the Wiener-Hopf technique and involves an infinite series of unknowns which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the problem parameters, whereby the effects of these parameters on the sound diffraction are studied. A perfect agreement is observed when the results of radiated field are compared numerically with a similar work existing in the literature.

8

Second-order linear state space systems: computeing the transfer funcion using the DFT

80%

Antoniou G. E.

Archives of Control Sciences

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2004

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tom Vol. 14, no. 1

5-13

EN

In this paper the discrete Fournier transform (DFT) is used for determining the transfer function coefficients for second-order linear systems (...). The proposed algorithm is theoretically attractive, practically fast and has been implemeted in Matlab. Two step-by-step examples illustrating the application of the algorithm are given.

9

Steganographic algorithm of hiding information in sound based on Fourier transform and masking

80%

Kozieł G.

Control and Cybernetics

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2011

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tom Vol. 40, no 4

1231-1247

EN

A new steganographicmethod based on Fourier transform is proposed. Data is attached in the frequency domain within the limits of the audible band. Masked frequencies are used to conceal information in order to make the changes inaudible for human ear. This approach allows for modification in the sound frequency band only, and does not require any additional modifications. It also allows for concealing information efficiently, minimizing the number of changes and gaining robustness with respect to popular sound transformations.

10

Inversion of the Riemann-Liouville operator and its dual using wavelets

80%

Baccar C. , Hamadi N. B. , Herch H. , Meherzi F.

Opuscula Mathematica

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2015

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tom Vol. 35, no. 6

867--887

EN

We define and study the generalized continuous wavelet transform associated with the Riemann-Liouville operator that we use to express the new inversion formulas of the Riemann-Liouville operator and its dual.

11

Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces

80%

Brandolini L. , Colzani L.

Colloquium Mathematicum

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1996

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tom 71

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nr 2

273-286

12

Template Matching Using Improved Rotations Fourier Transform Method

80%

Wijaya M. C.

International Journal of Electronics and Telecommunications

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2022

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tom Vol. 68. No. 4

881--888

EN

Template matching is a process to identify and localize a template image on an original image. Several methods are commonly used for template matching, one of which uses the Fourier transform. This study proposes a modification of the method by adding an improved rotation to the Fourier transform. Improved rotation in this study uses increment rotation and three shear methods for the template image rotation process. The three shear rotation method has the advantage of precise and noisefree rotation results, making the template matching process even more accurate. Based on the experimental results, the use of 10°angle increments has increased template matching accuracy. In addition, the use of three shear rotations can improve the accuracy of template matching by 13% without prolonging the processing time.

13

One shot profilometry using iterative two-step temporal phase-unwrapping

80%

Du G. , Wang M. , Zhou C. , Si S. , Li H. , Lei Z. , Li Y.

Optica Applicata

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2017

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tom Vol. 47, nr 1

97--110

EN

This paper reviews two techniques that have been recently published for three-dimensional profilometry and proposes one shot profilometry using iterative two-step temporal phase-unwrapping by combining the composite fringe projection and the iterative two-step temporal phase unwrapping algorithm. In temporal phase unwrapping, many images with different frequency fringe pattern are needed to project, which would take much time. In order to solve this problem, Ochoa proposed a phase unwrapping algorithm based on phase partitions using a composite fringe. However, we found that the fringe order determined through the construction of phase partitions tended to be imprecise. Recently, we proposed an iterative two-step temporal phase unwrapping algorithm, which can achieve high sensitivity and high precision shape measurement. But it needs multiple frames of fringe images which would take much time. In order to take into account both the speed and accuracy of three-dimensional shape measurement, we get a new, and more accurate unwrapping method based on a composite fringe pattern by combining these two techniques. This method not only retains the speed advantage of Ochoa’s algorithm, but also greatly improves its measurement accuracy. Finally, the experimental evaluation is conducted to prove the validity of the proposed method.

14

The method of determining the main harmonic frequency component

80%

Szczepański T. , Traczyk S. , Dziedziak P.

Transport Samochodowy

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2021

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tom z. 1

38--42

EN

Analysis of vibroacoustic signals is one of the more frequently used diagnostic methods for mechanical devices occurring, among the others, in the car diagnostics. Often, it happens that the most important element of the recorded course is the fundamental harmonic frequency of vibrations. Fundamental frequency indicates the main process related to the operation of the device and allows to follow its course. In the article the author’s method of determining the fundamental frequency in the signal, being the subject of a patent application, will be presented. Its theoretical basis and application examples were discussed comparing the accuracy of its use with the accuracy of other methods. The frequency range where the method finds application is shown. That is, where its accuracy turns out to be better than the accuracy of popular methods used to determine fundamental harmonic frequency component.

PL

Analiza sygnałów wibroakustycznych jest jedną z częściej stosowanych metod diagnostycznych urządzeń mechanicznych, występującą między innymi w diagnostyce samochodowej. Często zdarza się, że najbardziej istotnym elementem rejestrowanego przebiegu jest główna składowa harmoniczna drgań. Dominująca częstotliwość świadczy bowiem o głównym procesie związanym z pracą urządzenia i pozwala śledzić jego przebieg. W artykule zostanie przedstawiona autorska metoda wyznaczania głównej częstotliwości występującej w sygnale, będąca przedmiotem zgłoszenia patentowego. Omówiono jej podstawy teoretyczne oraz przykłady zastosowania, porównując dokładność jej stosowania z dokładnością innych metod. Wskazano na zakres częstotliwości, gdzie metoda znajduje zastosowanie, to znaczy gdzie jej dokładność okazuje się lepsza, niż dotychczas stosowanych sposobów wyznaczania głównej składowej harmonicznej.

15

Amplitude demodulation of interferometric signals with a 2D Hilbert transform

80%

Wielgus M.

Challenges of Modern Technology

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2011

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tom Vol. 2, no. 1

8--11

EN

The Hilbert transform and the analytic signal are widely known tools of 1D signal pro cessing. They are useful for many applications, such as AM-FM demodulation or edge detection. Developing the multidimensional generalization of this method is particularly important for the purposes of image processing. Unfortunately, it is not obvious how to generalize the transform, keeping its essential properties. In this paper I survey some ideas: basic approaches with spectral masks imitating 1D signum function, the spiral phase operator method and the method involving quaternionic Fourier transform. I present and compare how these algorithms are useful for the amplitude demodulation of typical interferometric images.

16

Investigating advantages and disadvantages of the analysis of a geometrical surface structure with the use of Fourier and wavelet transform

80%

Adamczak S. , Makieła W. , Stępień K.

Metrology and Measurement Systems

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2010

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tom Vol. 17, nr 2

233-243

EN

Nowadays a geometrical surface structure is usually evaluated with the use of Fourier transform. This type of transform allows for accurate analysis of harmonic components of surface profiles. Due to its fundamentals, Fourier transform is particularly efficient when evaluating periodic signals. Wavelets are the small waves that are oscillatory and limited in the range. Wavelets are special type of sets of basis functions that are useful in the description of function spaces. They are particularly useful for the description of non-continuous and irregular functions that appear most often as responses of real physical systems. Bases of wavelet functions are usually well located in the frequency and in the time domain. In the case of periodic signals, the Fourier transform is still extremely useful. It allows to obtain accurate information on the analyzed surface. Wavelet analysis does not provide as accurate information about the measured surface as the Fourier transform, but it is a useful tool for detection of irregularities of the profile. Therefore, wavelet analysis is the better way to detect scratches or cracks that sometimes occur on the surface. The paper presents the fundamentals of both types of transform. It presents also the comparison of an evaluation of the roundness profile by Fourier and wavelet transforms.

17

On a space of entire functions rapidly decreasing on Rn and its Fourier transform

80%

Musin I. d. K.

Concrete Operators

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2015

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tom 2

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nr 1

EN

A space of entire functions of several complex variables rapidly decreasing on Rn and such that their growth along iRn is majorized with the help of a family of weight functions is considered in this paper. For such space an equivalent description in terms of estimates on all of its partial derivatives as functions on Rn and a Paley-Wiener type theorem are obtained.

18

On the SU(2)×SU(2) symmetry in the Hubbard model

80%

Jakubczyk D. , Jakubczyk P.

Open Physics

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2012

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tom 10

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nr 4

906-912

EN

We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.

19

Fourier transform computation algorithm with regularization

80%

Emets V. , Rogowski J.

Przegląd Elektrotechniczny

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2010

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tom R. 86, nr 1

175-177

EN

Regularization theory for calculation of the Fourier transformations of continuous functions that vanish at infinity is considered. Procedure is based on using of the Gauss means. The regularization parameter is simple connected with error level of input data.

PL

W artykule przedstawiono teorię obliczania transformaty Fouriera funkcji ciągłych i zanikających w nieskończoności. Procedura jest oparta o wykorzystanie średnich Gaussa. Parametr regularyzacji jest połączony w prosty sposób z poziomem błędu danych wejściowych.

20

Boehmians of type S and their Fourier transforms

80%

Bhuvaneswari R. , Karunakaran V.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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2010

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tom 64

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nr 1

EN

Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.