Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem
Considering 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 theore...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2014
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/9036
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/9036
- Palabra clave:
- Fractional correlation
Fractional power spectrum
Ractional Fourier transform
Sampling theorem
Stochastic processes
Power spectral density
Random processes
Fractional correlation
Fractional Fourier transforms
Fractional power
Fractional power spectral density
Fractional sampling
Interpolation formulas
Sampling theorems
Stationary random signal
Digital signal processing
- Rights
- restrictedAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem |
| title |
Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem |
| spellingShingle |
Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem Fractional correlation Fractional power spectrum Ractional Fourier transform Sampling theorem Stochastic processes Power spectral density Random processes Fractional correlation Fractional Fourier transforms Fractional power Fractional power spectral density Fractional sampling Interpolation formulas Sampling theorems Stationary random signal Digital signal processing |
| title_short |
Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem |
| title_full |
Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem |
| title_fullStr |
Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem |
| title_full_unstemmed |
Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem |
| title_sort |
Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem |
| dc.subject.keywords.none.fl_str_mv |
Fractional correlation Fractional power spectrum Ractional Fourier transform Sampling theorem Stochastic processes Power spectral density Random processes Fractional correlation Fractional Fourier transforms Fractional power Fractional power spectral density Fractional sampling Interpolation formulas Sampling theorems Stationary random signal Digital signal processing |
| topic |
Fractional correlation Fractional power spectrum Ractional Fourier transform Sampling theorem Stochastic processes Power spectral density Random processes Fractional correlation Fractional Fourier transforms Fractional power Fractional power spectral density Fractional sampling Interpolation formulas Sampling theorems Stationary random signal Digital signal processing |
| description |
Considering 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. |
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2014 |
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2014 |
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2020-03-26T16:32:49Z |
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2020-03-26T16:32:49Z |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Artículo |
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IEEE Transactions on Signal Processing; Vol. 62, Núm. 14; pp. 3695-3705 |
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1053587X |
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https://hdl.handle.net/20.500.12585/9036 |
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10.1109/TSP.2014.2328977 |
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Universidad Tecnológica de Bolívar |
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Repositorio UTB |
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56270896900 8330328300 35094573000 |
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IEEE Transactions on Signal Processing; Vol. 62, Núm. 14; pp. 3695-3705 1053587X 10.1109/TSP.2014.2328977 Universidad Tecnológica de Bolívar Repositorio UTB 56270896900 8330328300 35094573000 |
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https://hdl.handle.net/20.500.12585/9036 |
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eng |
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eng |
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Atribución-NoComercial 4.0 Internacional |
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Recurso electrónico |
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Institute of Electrical and Electronics Engineers Inc. |
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Institute of Electrical and Electronics Engineers Inc. |
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2020-03-26T16:32:49Z2020-03-26T16:32:49Z2014IEEE Transactions on Signal Processing; Vol. 62, Núm. 14; pp. 3695-37051053587Xhttps://hdl.handle.net/20.500.12585/903610.1109/TSP.2014.2328977Universidad Tecnológica de BolívarRepositorio UTB56270896900833032830035094573000Considering 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.Recurso electrónicoapplication/pdfengInstitute of Electrical and Electronics Engineers Inc.http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_16echttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84903694215&doi=10.1109%2fTSP.2014.2328977&partnerID=40&md5=0cb6bcebd7e51b7bb66bab03e6173451Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theoreminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Fractional correlationFractional power spectrumRactional Fourier transformSampling theoremStochastic processesPower spectral densityRandom processesFractional correlationFractional Fourier transformsFractional powerFractional power spectral densityFractional samplingInterpolation formulasSampling theoremsStationary random signalDigital signal processingTorres R.Lizarazo Z.Torres E.Kotel'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. 14Shannon, C.E., A mathematical theory of communication (1948) Bell Syst. Tech. J., 27, pp. 379-423. , 623-656Jerri, A.J., The shannon sampling theorem-Its various extensions and applications: A tutorial review (1977) Proc. IEEE, 65 (11), pp. 1565-1596Xia, X.-G., On bandlimited signals with fractional fourier transform (1996) IEEE Signal Processing Letters, 3 (3), pp. 72-74. , PII S1070990896018366Namias, V., The fractional order Fourier transform and its application to quantum mechanics (1980) J. Inst. Math. Appl., 25, pp. 241-265Almeida, L.B., The fractional Fourier transform and time-frequency representations (1994) IEEE Trans. Signal Process., 42 (11), pp. 3084-3091. , NovLohmann, 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: ElsevierOzaktas, H.M., Zalevsky, Z., Kutay, M.A., (2001) The Fractional Fourier Transform with Applications in Optics and Signal Processing, , Chichester, U.K. WileyPellat-Finet, P., (2009) Optique de Fourier: Théorie Métaxiale et Fractionnaire (In French), , Paris, France: Springer-Verlag ParisAlmeida, L.B., Product and convolution theorems for the fractional Fourier transform (1997) IEEE Signal Processing Letters, 4 (1), pp. 15-17Zayed, A.I., A convolution and product theorem for the fractional Fourier transform (1998) IEEE Signal Processing Letters, 5 (4), pp. 101-103Akay, 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 S1053587X01022607Torres, R., Pellat-Finet, P., Torres, Y., Fractional convolution, fractional correlation and their translation invariance properties (2010) Signal Process., 90, pp. 1976-1984. , JunCandan, C., Ozaktas, H.M., Sampling and series expansion theorems for fractional Fourier and other transforms (2003) Signal Process., 83 (11), pp. 2455-2457Zayed, A.I., On the relationship between the Fourier and fractional Fourier transforms (1996) IEEE Signal Processing Letters, 3 (12), pp. 310-311. , PII S1070990896090347Zayed, A.I., Garcia, A.G., New sampling formulae for the fractional Fourier transform,"" (1999) Signal Process., 77 (1), pp. 111-114Torres, 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.2006.879470Wei, 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. 595-598Sharma, K., Comments on ""Generalized sampling expansion for bandlimited signals associated with fractional Fourier transform (2011) IEEE Signal Process. Lett., 18 (12), pp. 761-761Bhandari, A., Marziliano, P., Sampling and reconstruction of sparse signals in fractional Fourier domain (2010) IEEE Signal Process. Lett., 17 (3), pp. 221-224Wiener, 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 TechnolTao, R., Zhang, F., Wang, Y., Fractional power spectrum (2008) IEEE Trans. Signal Process., 56, pp. 4199-4206. , SepTorres, 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. 1555-1560Wiener, N., Generalized harmonic analysis (1930) Acta Mathematica, 55 (1), pp. 117-258Khintchine, A., Korrelationstheorie der stationären stochastischen prozesse (1934) Mathematische Annalen, 109 (1), pp. 604-615Gardner, W., A sampling theorem for nonstationary random processes (corresp.) (1972) IEEE Trans. Inf. Theory, 18 (6), pp. 808-809Garcia, F.M., Lourtie, I.M., Buescu, J., Nonstationary processes and the sampling theorem (2001) IEEE Signal Process. Lett., 8 (4), pp. 117-119Tao, R., Zhang, F., Wang, Y., Sampling random signals in a fractional Fourier domain (2011) Signal Process., 91 (6), pp. 1394-1400Wei, D., Li, Y., Sampling reconstruction of n-dimensional bandlimited images after multilinear filtering in fractional Fourier domain (2013) Opt. Commun., 295, pp. 26-35Hopf, E., (1937) Ergodentheorie (In German), Ser. Ergebnisse der Mathematik und Ihrer Grenzgebiete 5 Bd., 5 (2). , Berlin, Germany: Julius SpringerWalters, P., Walters, P., (1982) An Introduction to Ergodic Theory, 79. , New York, NY, USA: Springer-VerlagNeumann, J.V., Proof of the quasi-ergodic hypothesis (1932) Proc. Nat. Acad. Sci. USA, 18 (1), p. 70Doob, J., (1990) , Stochastic Processes, Ser., , Wiley Publications in Statistics. New York, NY, USA: WileyBirkhoff, G.D., Proof of the ergodic theorem (1931) Proc. Nat. Acad. Sci. USA, 17 (12), pp. 656-660Krengel, U., Brunel, A., (1985) Ergodic Theorems, Ser. de Gruyter Studies in Mathematics, , Berlin, Germany: W. de GruyterBhandari, A., Zayed, A.I., Shift-invariant and sampling spaces associated with the fractional Fourier transform domain (2012) IEEE Trans. Signal Process., 60 (4), pp. 1627-1637Casinovi, G., Sampling and ergodic theorems for weakly almost periodic signals (2009) IEEE Trans. Inf. Theory, 55 (4), pp. 1883-1897. , AprMcBride, A.C., Kerr, F.H., On namias's fractional Fourier transforms (1987) IMA J. Appl. Math., 39 (2), pp. 159-175Lohmann, A.W., Image rotation, Wigner rotation, and the fractional Fourier transform (1993) J. Opt. Soc. Amer. A, 10, pp. 2181-2186. , OctBoashash, B., (2003) Time Frequency Signal Analysis and Processing, , New York, NY, USA: Elsevier ScienceHlawatsch, F., Matz, G., Time-frequency methods for non-stationary statistical signal processing (2010) Time-Frequency Analysis: Concepts and Methods, pp. 279-320. , http://dx.doi.org/10.1002/9780470611203.ch10, London, U.K.: ISTEhttp://purl.org/coar/resource_type/c_6501THUMBNAILMiniProdInv.pngMiniProdInv.pngimage/png23941https://repositorio.utb.edu.co/bitstream/20.500.12585/9036/1/MiniProdInv.png0cb0f101a8d16897fb46fc914d3d7043MD5120.500.12585/9036oai:repositorio.utb.edu.co:20.500.12585/90362021-02-02 14:03:01.856Repositorio Institucional UTBrepositorioutb@utb.edu.co |