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Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem

dc.creatorTorres R.
dc.creatorLizarazo Z.
dc.creatorTorres E.
dc.identifier.citationIEEE Transactions on Signal Processing; Vol. 62, Núm. 14; pp. 3695-3705
dc.description.abstractConsidering that fractional correlation function and the fractional power spectral density, for -stationary random signals, form a fractional Fourier transform pair. We present an interpolation formula to estimate a random signal from a temporal random series, based on the fractional sampling theorem for -bandlimited random signals. Furthermore, by establishing the relationship between the sampling theorem and the von Neumann ergodic theorem, the estimation of the power spectral density of a random signal from one sample signal becomes a suitable approach. Thus, the validity of the sampling theorem for random signals is closely linked to an ergodic hypothesis in the mean sense. © 2014 IEEE.eng
dc.format.mediumRecurso electrónico
dc.publisherInstitute of Electrical and Electronics Engineers Inc.
dc.titleFractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem
dcterms.bibliographicCitationKotel'nikov, V.A., On the transmission capacity of ether and wire in electro-communications (1933) Proc. 1st All-Union Conf. Questions of Commun., pp. 1-19. , Jan. 14
dcterms.bibliographicCitationShannon, C.E., A mathematical theory of communication (1948) Bell Syst. Tech. J., 27, pp. 379-423. , 623-656
dcterms.bibliographicCitationJerri, A.J., The shannon sampling theorem-Its various extensions and applications: A tutorial review (1977) Proc. IEEE, 65 (11), pp. 1565-1596
dcterms.bibliographicCitationXia, X.-G., On bandlimited signals with fractional fourier transform (1996) IEEE Signal Processing Letters, 3 (3), pp. 72-74. , PII S1070990896018366
dcterms.bibliographicCitationNamias, V., The fractional order Fourier transform and its application to quantum mechanics (1980) J. Inst. Math. Appl., 25, pp. 241-265
dcterms.bibliographicCitationAlmeida, L.B., The fractional Fourier transform and time-frequency representations (1994) IEEE Trans. Signal Process., 42 (11), pp. 3084-3091. , Nov
dcterms.bibliographicCitationLohmann, A.W., Mendlovic, D., Zalevsky, Z., (1998) IV: Fractional Transformations in Optics, Ser. Progress in Optics, 38, pp. 263-342. , E.Wolf, Ed. New York, NY, USA: Elsevier
dcterms.bibliographicCitationOzaktas, H.M., Zalevsky, Z., Kutay, M.A., (2001) The Fractional Fourier Transform with Applications in Optics and Signal Processing, , Chichester, U.K. Wiley
dcterms.bibliographicCitationPellat-Finet, P., (2009) Optique de Fourier: Théorie Métaxiale et Fractionnaire (In French), , Paris, France: Springer-Verlag Paris
dcterms.bibliographicCitationAlmeida, L.B., Product and convolution theorems for the fractional Fourier transform (1997) IEEE Signal Processing Letters, 4 (1), pp. 15-17
dcterms.bibliographicCitationZayed, A.I., A convolution and product theorem for the fractional Fourier transform (1998) IEEE Signal Processing Letters, 5 (4), pp. 101-103
dcterms.bibliographicCitationAkay, O., Boudreaux-Bartels, G.F., Fractional convolution and correlation via operator methods and an application to detection of linear FM signals (2001) IEEE Transactions on Signal Processing, 49 (5), pp. 979-993. , DOI 10.1109/78.917802, PII S1053587X01022607
dcterms.bibliographicCitationTorres, R., Pellat-Finet, P., Torres, Y., Fractional convolution, fractional correlation and their translation invariance properties (2010) Signal Process., 90, pp. 1976-1984. , Jun
dcterms.bibliographicCitationCandan, C., Ozaktas, H.M., Sampling and series expansion theorems for fractional Fourier and other transforms (2003) Signal Process., 83 (11), pp. 2455-2457
dcterms.bibliographicCitationZayed, A.I., On the relationship between the Fourier and fractional Fourier transforms (1996) IEEE Signal Processing Letters, 3 (12), pp. 310-311. , PII S1070990896090347
dcterms.bibliographicCitationZayed, A.I., Garcia, A.G., New sampling formulae for the fractional Fourier transform,"" (1999) Signal Process., 77 (1), pp. 111-114
dcterms.bibliographicCitationTorres, R., Pellat-Finet, P., Torres, Y., Sampling theorem for fractional bandlimited signals: A self-contained proof. Application to digital holography (2006) IEEE Signal Processing Letters, 13 (11), pp. 676-679. , DOI 10.1109/LSP.2006.879470
dcterms.bibliographicCitationWei, D., Ran, Q., Li, Y., Generalized sampling expansion for bandlimited signals associated with the fractional Fourier transform (2010) IEEE Signal Process. Lett., 17 (6), pp. 595-598
dcterms.bibliographicCitationSharma, K., Comments on ""Generalized sampling expansion for bandlimited signals associated with fractional Fourier transform (2011) IEEE Signal Process. Lett., 18 (12), pp. 761-761
dcterms.bibliographicCitationBhandari, A., Marziliano, P., Sampling and reconstruction of sparse signals in fractional Fourier domain (2010) IEEE Signal Process. Lett., 17 (3), pp. 221-224
dcterms.bibliographicCitationWiener, N., (1964) Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications, , ser. Technology press books in science and engineering. Cambridge, MA, USA: Technology Press of the Mass. Inst. of Technol
dcterms.bibliographicCitationTao, R., Zhang, F., Wang, Y., Fractional power spectrum (2008) IEEE Trans. Signal Process., 56, pp. 4199-4206. , Sep
dcterms.bibliographicCitationTorres, R., Torres, E., Fractional Fourier analysis of random signals and the notion of -stationarity of the Wigner-Ville distribution (2013) IEEE Trans. Signal Process., 61 (6), pp. 1555-1560
dcterms.bibliographicCitationWiener, N., Generalized harmonic analysis (1930) Acta Mathematica, 55 (1), pp. 117-258
dcterms.bibliographicCitationKhintchine, A., Korrelationstheorie der stationären stochastischen prozesse (1934) Mathematische Annalen, 109 (1), pp. 604-615
dcterms.bibliographicCitationGardner, W., A sampling theorem for nonstationary random processes (corresp.) (1972) IEEE Trans. Inf. Theory, 18 (6), pp. 808-809
dcterms.bibliographicCitationGarcia, F.M., Lourtie, I.M., Buescu, J., Nonstationary processes and the sampling theorem (2001) IEEE Signal Process. Lett., 8 (4), pp. 117-119
dcterms.bibliographicCitationTao, R., Zhang, F., Wang, Y., Sampling random signals in a fractional Fourier domain (2011) Signal Process., 91 (6), pp. 1394-1400
dcterms.bibliographicCitationWei, D., Li, Y., Sampling reconstruction of n-dimensional bandlimited images after multilinear filtering in fractional Fourier domain (2013) Opt. Commun., 295, pp. 26-35
dcterms.bibliographicCitationHopf, E., (1937) Ergodentheorie (In German), Ser. Ergebnisse der Mathematik und Ihrer Grenzgebiete 5 Bd., 5 (2). , Berlin, Germany: Julius Springer
dcterms.bibliographicCitationWalters, P., Walters, P., (1982) An Introduction to Ergodic Theory, 79. , New York, NY, USA: Springer-Verlag
dcterms.bibliographicCitationNeumann, J.V., Proof of the quasi-ergodic hypothesis (1932) Proc. Nat. Acad. Sci. USA, 18 (1), p. 70
dcterms.bibliographicCitationDoob, J., (1990) , Stochastic Processes, Ser., , Wiley Publications in Statistics. New York, NY, USA: Wiley
dcterms.bibliographicCitationBirkhoff, G.D., Proof of the ergodic theorem (1931) Proc. Nat. Acad. Sci. USA, 17 (12), pp. 656-660
dcterms.bibliographicCitationKrengel, U., Brunel, A., (1985) Ergodic Theorems, Ser. de Gruyter Studies in Mathematics, , Berlin, Germany: W. de Gruyter
dcterms.bibliographicCitationBhandari, A., Zayed, A.I., Shift-invariant and sampling spaces associated with the fractional Fourier transform domain (2012) IEEE Trans. Signal Process., 60 (4), pp. 1627-1637
dcterms.bibliographicCitationCasinovi, G., Sampling and ergodic theorems for weakly almost periodic signals (2009) IEEE Trans. Inf. Theory, 55 (4), pp. 1883-1897. , Apr
dcterms.bibliographicCitationMcBride, A.C., Kerr, F.H., On namias's fractional Fourier transforms (1987) IMA J. Appl. Math., 39 (2), pp. 159-175
dcterms.bibliographicCitationLohmann, A.W., Image rotation, Wigner rotation, and the fractional Fourier transform (1993) J. Opt. Soc. Amer. A, 10, pp. 2181-2186. , Oct
dcterms.bibliographicCitationBoashash, B., (2003) Time Frequency Signal Analysis and Processing, , New York, NY, USA: Elsevier Science
dcterms.bibliographicCitationHlawatsch, F., Matz, G., Time-frequency methods for non-stationary statistical signal processing (2010) Time-Frequency Analysis: Concepts and Methods, pp. 279-320. ,, London, U.K.: ISTE
dc.subject.keywordsFractional correlation
dc.subject.keywordsFractional power spectrum
dc.subject.keywordsRactional Fourier transform
dc.subject.keywordsSampling theorem
dc.subject.keywordsStochastic processes
dc.subject.keywordsPower spectral density
dc.subject.keywordsRandom processes
dc.subject.keywordsFractional correlation
dc.subject.keywordsFractional Fourier transforms
dc.subject.keywordsFractional power
dc.subject.keywordsFractional power spectral density
dc.subject.keywordsFractional sampling
dc.subject.keywordsInterpolation formulas
dc.subject.keywordsSampling theorems
dc.subject.keywordsStationary random signal
dc.subject.keywordsDigital signal processing
dc.rights.ccAtribución-NoComercial 4.0 Internacional
dc.identifier.instnameUniversidad Tecnológica de Bolívar
dc.identifier.reponameRepositorio UTB

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