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Academic literature on the topic 'Hilbert transform'

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Published: 4 June 2021
Last updated: 28 July 2024

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Journal articles on the topic "Hilbert transform"

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Liflyand, Elijah. "Fourier transform versus Hilbert transform." Journal of Mathematical Sciences 187, no. 1 (October 14, 2012): 49–56. http://dx.doi.org/10.1007/s10958-012-1048-0.

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Bertie, John E., and Shuliang L. Zhang. "Infrared intensities of liquids. IX. The Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 520–31. http://dx.doi.org/10.1139/v92-074.

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It is well known that the infinite Kramers–Kronig transform is equivalent to the infinite Hilbert transform, which is equivalent to the allied Fourier integrals. The Hilbert transform can thus be implemented using fast Fourier transform routines. Such implementation is usually some 60 times faster than the Kramers–Kronig transform for a data file containing about 7 points. This paper reports that, for transformations between the real and imaginary refractive indices, [Formula: see text] and [Formula: see text] in [Formula: see text], the FFT-based Hilbert transform can be much less accurate than, or as accurate as, the Kramers–Kronig transform, depending on the algorithm used. The Kramers–Kronig transform, incorporating Mclaurin's formula for finding the principal value of the integral, transforms [Formula: see text] spectra into [Formula: see text] spectra that are accurate to about 0.05%. Some Hilbert transform algorithms in the literature yield only about 4% accuracy. The BZ algorithm for the Hilbert transform is presented, for use on a laboratory computer running under DOS, that yields [Formula: see text] spectra accurate to 0.05%. For the transform from [Formula: see text] to [Formula: see text], the BZ algorithm gives [Formula: see text] accurate to about −0.2% of the largest k value in the spectrum. This compares with an accuracy of 0.5% for the Kramers–Kronig transform. In cases where the [Formula: see text] spectrum is truncated at low wavenumbers, a simple method is presented that improves by a factor of ~10 the accuracy at low wavenumber of the [Formula: see text] spectrum obtained by Hilbert or Kramers–Kronig transforms of the [Formula: see text] spectrum. Keywords: infrared intensities, complex refractive indices, Kramers–Kronig transform, Hilbert transform, optical constants.
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Aliev, Rashid, and Lale Alizade. "Approximation of the Hilbert transform in the Lebesgue spaces." Journal of Numerical Analysis and Approximation Theory 52, no. 2 (December 28, 2023): 139–54. http://dx.doi.org/10.33993/jnaat522-1312.

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The Hilbert transform plays an important role in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the real and imaginary components, and the magnitude and phase components of spectra. The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform is the main part of the singular integral equations on the real line. Therefore, approximations of the Hilbert transform are of great interest. Many papers have dealt with the numerical approximation of the singular integrals in the case of bounded intervals. On the other hand, the literature concerning the numerical integration on unbounded intervals is by far poorer than the one on bounded intervals. The case of the Hilbert Transform has been considered very little. This article is devoted to the approximation of the Hilbert transform in Lebesgue spaces by operators which introduced by V.R.Kress and E.Mortensen to approximate the Hilbert transform of analytic functions in a strip. In this paper, we prove that the approximating operators are bounded maps in Lebesgue spaces and strongly converges to the Hilbert transform in these spaces.
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Munadi, Suprajitno. "Fast Hilbert Transform." Scientific Contributions Oil and Gas 11, no. 1 (April 13, 2022): 4–16. http://dx.doi.org/10.29017/scog.11.1.894.

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The use of Hilbert Transform is becoming more and more Important for analysis and processing of geophysical data. However, the direct mathematical formulation in the form of contour integration is not easy to pro. A specific formulation which relates the Hilbert transform and the Fourier transform has been established for developing a computer Programme. This relationship enables us to execute the Hilbert Transformation in a very quick manner using the well known Fast Fourier transform algorithm.The application of this method for generating quadrature seismic trace and recovering minimum phase specimum from the magnitude demonstrates the effectiveness of the programme. The conversion of non-minimum phase seismic wavelet whichas similar spectral magnitude can be done using the hilbert transform.
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Lohmann, Adolf W., David Mendlovic, and Zeev Zalevsky. "Fractional Hilbert transform." Optics Letters 21, no. 4 (February 15, 1996): 281. http://dx.doi.org/10.1364/ol.21.000281.

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Huang, Norden, Zhaohua Wu, and Steven Long. "Hilbert-Huang transform." Scholarpedia 3, no. 7 (2008): 2544. http://dx.doi.org/10.4249/scholarpedia.2544.

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Wang, Yan Hai. "The Local Fractional Hilbert Transform Based on Fractal Theory." Advanced Materials Research 998-999 (July 2014): 996–99. http://dx.doi.org/10.4028/www.scientific.net/amr.998-999.996.

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In this paper, the local fractional Hilbert transform in fractal space is established. The characteristics of this local fractional transform are discussed in the following. Considering the basic properties of the local fractional Hilbert transforms, a kind of transform for local fractional is derived and analyzed.
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Abdullah, Naheed, and Saleem Iqbal. "The Fractional Hilbert Transform of Generalized Functions." Symmetry 14, no. 10 (October 8, 2022): 2096. http://dx.doi.org/10.3390/sym14102096.

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The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its widespread application in optics, engineering, and signal processing. In the present work, we expand the fractional Hilbert transform that displays an odd symmetry to a space of generalized functions known as Boehmians. Moreover, we introduce a new fractional convolutional operator for the fractional Hilbert transform to prove a convolutional theorem similar to the classical Hilbert transform, and also to extend the fractional Hilbert transform to Boehmians. We also produce a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate the convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.
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ALIEV, R. A., and L. G. SAMADOVA. "Boundedness of the discrete Hilbert transform in discrete Hölder spaces." Baku Mathematical Journal 2, no. 1 (March 1, 2023): 47–56. http://dx.doi.org/10.32010/j.bmj.2023.04.

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The Hilbert transform plays an important role in the theory and practice of signal processing operations in continuous system theory. The Hilbert transform was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in many areas of science and technology and plays an important role in digital signal processing. The essential motivation behind thinking about discrete transforms is that experimental data are most frequently not taken in a continuous manner but sampled at discrete time values. Since much of the data collected in both the physical sciences and engineering are discrete, the discrete Hilbert transform is a rather useful tool in these areas for the general analysis of this type of data. The Hilbert transform has been well studied on classical function spaces such as H¨older, Lebesgue, Morrey, etc. But its discrete version, which also has numerous applications, has not been fully studied in discrete analogues of these spaces. In this paper, we discuss the discrete Hilbert transform in discrete H¨older spaces and obtain its boundedness in these spaces.
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Dragomir, Silvestru. "Inequalities for a generalized finite Hilbert transform of convex functions." Mathematica Moravica 25, no. 2 (2021): 81–96. http://dx.doi.org/10.5937/matmor2102081s.

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Dissertations / Theses on the topic "Hilbert transform"

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Cervi, Jacopo. "Hilbert transform." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7466/.

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The Hilbert transform is an important tool in both pure and applied mathematics. It is largely used in the field of signal processing. Lately has been used in mathematical finance as the fast Hilbert transform method is an efficient and accurate algorithm for pricing discretely monitored barrier and Bermudan style options. The purpose of this report is to show the basic properties of the Hilbert transform and to check the domain of definition of this operator.
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Husin, Axel. "The Hilbert Transform." Thesis, Uppsala universitet, Analys och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-200442.

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Barnhart, Bradley Lee. "The Hilbert-Huang Transform: theory, applications, development." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/2670.

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Hilbert-Huang Transform (HHT) is a data analysis tool, first developed in 1998, which can be used to extract the periodic components embedded within oscillatory data. This thesis is dedicated to the understanding, application, and development of this tool. First, the background theory of HHT will be described and compared with other spectral analysis tools. Then, a number of applications will be presented, which demonstrate the capability for HHT to dissect and analyze the periodic components of different oscillatory data. Finally, a new algorithm is presented which expands HHT ability to analyze discontinuous data. The sum result is the creation of a number of useful tools developed from the application of HHT, as well as an improvement of the HHT tool itself.
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Li, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.

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Ariyani, Mathematics &amp Statistics Faculty of Science UNSW. "The generalized continuous wavelet transform on Hilbert modules." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/42151.

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The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform.
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Navarro, Moisés M. "Ocean wave data analysis using Hilbert transform techniques." Thesis, Monterey, California. Naval Postgraduate School, 1996. http://hdl.handle.net/10945/32022.

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A novel technique to determine the phase velocity of long-wavelength shoaling waves is investigated. Operationally, the technique consists of three steps. First, using the Hilbert transform of a time series, the phase of the analytic signal is determined. Second, the correlations of the phases of analytic signals between two points in space are calculated and an average time of travel of the wave fronts is obtained. Third, if directional spectra are available or can be determined from time series of large array of buoys, the angular information can be used to determine the true time of travel. The phase velocity is obtained by dividing the distance between buoys by the correlation time. Using the Hilbert transform approach, there is no explicit assumption of the relation between frequency and wavenumber of waves in the wave field, indicating that it may be applicable to arbitrary wave fields, both linear and nonlinear. Limitations of the approach are discussed.
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Eftekhar, Amir. "Hilbert-Huang transform : biosignal analysis and practical implementation." Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/5991.

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Any system, however trivial, is subjected to data analysis on the signals it produces. Over the last 50 years the influx of new techniques and expansions of older ones have allowed a number of new applications, in a variety of fields, to be analysed and to some degree understood. One of the industries that is benefiting from this growth is the medical field and has been further progressed with the growth of interdisciplinary collaboration. From a signal processing perspective, the challenge comes from the complex and sometimes chaotic nature of the signals that we measure from the body, such as those from the brain and to some degree the heart. In this work we will make a contribution to dealing with such systems, in the form of a recent time-frequency data analysis method, the Hilbert-Huang Transform (HHT), and extensions to it. This thesis presents an analysis of the state of the art in seizure and heart arrhythmia detection and prediction methods. We then present a novel real-time implementation of the algorithm both in software and hardware and the motivations for doing so. First, we present our software implementation, encompassing realtime capabilities and identifying elements that need to be considered for practical use. We then translated this software into hardware to aid real-time implementation and integration. With these implementations in place we apply the HHT method to the topic of epilepsy (seizures) and additionally make contributions to heart arrhythmias and neonate brain dynamics. We use the HHT and some additional algorithms to quantify features associated with each application for detection and prediction. We also quantify significance of activity in such a way as to merge prediction and detection into one framework. Finally, we assess the real-time capabilities of our methods for practical use as a biosignal analysis tool.
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Hollenbeck, Brian. "Best constants for operators involving the Hilbert transform /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3012977.

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Liu, Yue Lin. "The linear canonical transform and generalized hilbert transform with applications in signal processing." Thesis, University of Macau, 2009. http://umaclib3.umac.mo/record=b2100798.

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Agora, Elona. "Boundedness of the Hilbert Transform on Weighted Lorentz Spaces." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/108930.

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The main goal of this thesis is to characterize the weak-type (resp. strong-type) boundedness of the Hilbert transform H on weighted Lorentz spaces Λpu(w). The characterization is given in terms of some geometric conditions on the weights u and w and the weak-type (resp. strong-type) boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results extend and unify simultaneously the theory of the boundedness of H on weighted Lebesgue spaces Lp(u) and Muckenhoupt weights Ap, and the theory on classical Lorentz spaces Λp(w) and Ariño-Muckenhoupt weights Bp.
Títol: Acotaciò de l'operador de Hilbert sobre espais de Lorentz amb pesos Resum: L'objectiu principal d'aquesta tesi es caracteritzar l'acotació de l'operador de Hilbert sobre els espais de Lorentz amb pesos Λpu(w). També estudiem la versió dèbil. La caracterització es dona en terminis de condicions geomètriques sobre els pesos u i w, i l'acotació de l'operador maximal de Hardy-Littlewood sobre els mateixos espais. Els nostres resultats unifiquen dues teories conegudes i aparentment no relacionades entre elles, que tracten l'acotació de l'operador de Hilbert sobre els espais de Lebegue amb pesos Lp(u) per una banda i els espais de Lorentz clàssics Λp(w) per altre banda.
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Books on the topic "Hilbert transform"

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King, Frederick W. Hilbert transforms. New York: Cambridge University Press, 2008.

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Feldman, Michael. Hilbert transform applications in mechanical vibration. Chichester: Wiley, 2011.

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Feldman, Michael. Hilbert Transform Applications in Mechanical Vibration. Chichester, UK: John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9781119991656.

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1937-, Huang N. E., and Attoh-Okine Nii O, eds. The Hilbert-Huang transform in engineering. New York: Taylor & Francis, 2005.

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Hahn, Stefan L. Hilbert transforms in signal processing. Boston: Artech House, 1996.

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Volland, Dominik. A Discrete Hilbert Transform with Circle Packings. Wiesbaden: Springer Fachmedien Wiesbaden, 2017. http://dx.doi.org/10.1007/978-3-658-20457-0.

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1937-, Huang N. E., and Shen Samuel S, eds. The Hilbert-Huang transform and its applications. New Jersey: World Scientific, 2005.

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Kim, Joonil. Multiple-Hilbert transforms associated with polynomials. Providence, Rhode Island: American Mathematical Society, 2015.

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King, Nigel E. Detection of structural nonlinearity using Hilbert transform procedures. Manchester: University of Manchester, 1994.

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Pandey, J. N. The Hilbert Transform of Schwartz Distributions and Applications. Hoboken, NJ, USA: John Wiley & Sons, Inc., 1995. http://dx.doi.org/10.1002/9781118032510.

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Book chapters on the topic "Hilbert transform"

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Kido, Ken’iti. "Hilbert Transform." In Digital Fourier Analysis: Advanced Techniques, 105–30. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1127-1_5.

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Layer, Edward, and Krzysztof Tomczyk. "Hilbert Transform." In Signal Transforms in Dynamic Measurements, 107–16. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-13209-9_6.

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Liflyand, Elijah. "Hilbert Transform." In Pathways in Mathematics, 71–99. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81892-0_5.

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Dickman, Arie. "Hilbert Transform." In Verified Signal Processing Algorithms in Matlab and C, 125–26. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93363-0_10.

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Arias de Reyna, Juan. "3. Hilbert Transform." In Lecture Notes in Mathematics, 31–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-45822-7_3.

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Volland, Dominik. "Discrete Hilbert Transform." In A Discrete Hilbert Transform with Circle Packings, 61–88. Wiesbaden: Springer Fachmedien Wiesbaden, 2017. http://dx.doi.org/10.1007/978-3-658-20457-0_5.

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Pereyra, María, and Lesley Ward. "The Hilbert transform." In Harmonic Analysis, 329–70. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/063/12.

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Duoandikoetxea, Javier. "The Hilbert transform." In Fourier Analysis, 49–68. Providence, Rhode Island: American Mathematical Society, 2000. http://dx.doi.org/10.1090/gsm/029/03.

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Duffy, Dean G. "The Hilbert Transform." In Advanced Engineering Mathematics, 195–215. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003272205-4.

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Liflyand, E. "Summability to the Hilbert Transform." In Operator Theory and Harmonic Analysis, 361–68. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77493-6_21.

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Conference papers on the topic "Hilbert transform"

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Schmitt, Jeremy, Nelly Pustelnik, Pierre Borgnat, and Patrick Flandrin. "2D Hilbert-Huang Transform." In ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2014. http://dx.doi.org/10.1109/icassp.2014.6854630.

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Kuwata, Seiichi. "Resolvent Based Hilbert Transform." In The 6th International Conference on Numerical Modelling in Engineering. Switzerland: Trans Tech Publications Ltd, 2024. http://dx.doi.org/10.4028/p-0dhwan.

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To perform the Hilbert transform Hil of a non-integrable function φ, such as φ(x) = 1, x, in a numerical calculation-friendly way, we propose a method of rewriting Hil in terms of the resolvent for a differential operator R whose eigenfunctions satisfy the orthogonality and the completeness, so that the resolvent kernel 〈x|R-1y〉can be given by the eigenfunction expansion. We deal with two cases for the choice of R: one is the harmonic oscillator Hamiltonian, which is commutative with the Fourier transform F; and the other is such that is commutative with Hil itself. We show how the calculation of Hilφ is made in a numerical calculation-friendly way, to find that Πk=0,1Hilfk (fk (x) = xk) satisfies quite a simple relation.
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Torres, M., Eduardo Tepichin-Rodriguez, Adolf W. Lohmann, David Sanchez, and Gustavo Ramirez Zabaleta. "Fractional Hilbert transform and isotropic Hilbert transform for two-dimensional objects: numerical simulation." In ICO XVIII 18th Congress of the International Commission for Optics, edited by Alexander J. Glass, Joseph W. Goodman, Milton Chang, Arthur H. Guenther, and Toshimitsu Asakura. SPIE, 1999. http://dx.doi.org/10.1117/12.354828.

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Bayraktar, Muharrem, and Meric Ozcan. "Hilbert transform based hologram filtering." In 2010 IEEE 18th Signal Processing and Communications Applications Conference (SIU). IEEE, 2010. http://dx.doi.org/10.1109/siu.2010.5652802.

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Boche, Holger, and Ullrich J. Monich. "Extension of the Hilbert transform." In ICASSP 2012 - 2012 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2012. http://dx.doi.org/10.1109/icassp.2012.6288719.

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Valluraiah, P., and B. Biswal. "ECG signal analysis using Hilbert transform." In 2015 IEEE Power, Communication and Information Technology Conference (PCITC). IEEE, 2015. http://dx.doi.org/10.1109/pcitc.2015.7438211.

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Vani H.Y and M. A. Anusuya. "Hilbert Huang transform based speech recognition." In 2016 Second International Conference on Cognitive Computing and Information Processing (CCIP). IEEE, 2016. http://dx.doi.org/10.1109/ccip.2016.7802858.

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Tanc, Yesim Hekim, and A. Akan. "Modulation classification by Hilbert-Huang Transform." In 2013 21st Signal Processing and Communications Applications Conference (SIU). IEEE, 2013. http://dx.doi.org/10.1109/siu.2013.6531183.

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Derakhshan, N., and M. H. Savoji. "Perceptual Speech Enhancement Using Hilbert Transform." In 2006 IEEE International Symposium on Industrial Electronics. IEEE, 2006. http://dx.doi.org/10.1109/isie.2006.295543.

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Song, Shi-De, Zhi-chao Yao, and Xiao-Na Wang. "The summary of Hilbert-Huang transform." In ISPDI 2013 - Fifth International Symposium on Photoelectronic Detection and Imaging, edited by Haimei Gong, Zelin Shi, Qian Chen, and Jin Lu. SPIE, 2013. http://dx.doi.org/10.1117/12.2033233.

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Reports on the topic "Hilbert transform"

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Cayse, Robert W. Application of the Hilbert Transform to Doppler Radar Signals from a Hypervelocity Gun. Fort Belvoir, VA: Defense Technical Information Center, April 1988. http://dx.doi.org/10.21236/ada193690.

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The invariants of the Hilbert transform data wavelet analysis. LJournal, 2016. http://dx.doi.org/10.18411/d-2016-159.

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