메뉴 건너뛰기




Volumn 31, Issue 1, 2012, Pages 301-312

A convolution and correlation theorem for the linear canonical transform and its application

Author keywords

Convolution theorem; Correlation theorem; Linear canonical transform; Sampling

Indexed keywords

BAND-LIMITED SIGNAL; CONVOLUTION STRUCTURE; CONVOLUTION THEOREMS; FILTER DESIGNS; FRACTIONAL FOURIER TRANSFORMS; LINEAR CANONICAL TRANSFORM; LOW-PASS; SAMPLING THEOREMS; UNIFORM SAMPLING;

EID: 84863077201     PISSN: 0278081X     EISSN: 15315878     Source Type: Journal    
DOI: 10.1007/s00034-011-9319-4     Document Type: Article
Times cited : (87)

References (28)
  • 1
    • 0028546432 scopus 로고
    • Optical operations on wave functions as the Abelian Subgroups of the special affine Fourier transformation
    • S. Abe, J.T. Sheridan, Optical operations on wave functions as the Abelian Subgroups of the special affine Fourier transformation. Opt. Lett. 19(22), 1801-1803 (1994)
    • (1994) Opt. Lett. , vol.19 , Issue.22 , pp. 1801-1803
    • Abe, S.1    Sheridan, J.T.2
  • 2
    • 0035340022 scopus 로고    scopus 로고
    • Fractional convolution and correlation via operator methods and an application to detection of linear FM signals
    • DOI 10.1109/78.917802, PII S1053587X01022607
    • O. Akay, G.F. Boudreaux-Bartels, Fractional convolution and correlation via operator methods and application to detection of linear FM signals. IEEE Trans. Signal Process. 49, 979-993 (2001) (Pubitemid 32444197)
    • (2001) IEEE Transactions on Signal Processing , vol.49 , Issue.5 , pp. 979-993
    • Akay, O.1    Boudreaux-Bartels, G.F.2
  • 3
    • 0028546458 scopus 로고
    • The fractional Fourier transform and time-frequency representations
    • L.B. Almeida, The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process. 42(11), 3084-3091 (1994)
    • (1994) IEEE Trans. Signal Process. , vol.42 , Issue.11 , pp. 3084-3091
    • Almeida, L.B.1
  • 4
    • 0030826059 scopus 로고    scopus 로고
    • Product and convolution theorems for the fractional Fourier transform
    • L.B. Almeida, Product and convolution theorems for the fractional Fourier transform. IEEE Signal Process. Lett. 4, 15-17 (1997) (Pubitemid 127554931)
    • (1997) IEEE Signal Processing Letters , vol.4 , Issue.1 , pp. 15-17
    • Almeida, L.B.1
  • 5
    • 0031079193 scopus 로고    scopus 로고
    • Optimal filtering with linear canonical transformations
    • PII S0030401896005986
    • B. Barshan, M.A. Kutay, H.M. Ozaktas, Optimal filtering with linear canonical transformations. Opt. Commun. 135, 32-36 (1997) (Pubitemid 127413994)
    • (1997) Optics Communications , vol.135 , Issue.1-3 , pp. 32-36
    • Barshan, B.1    Kutay, M.A.2    Ozaktas, H.M.3
  • 6
    • 0001484759 scopus 로고    scopus 로고
    • ABCD matrix formalism of fractional Fourier optics
    • L.M. Bernardo, ABCD matrix formalism of fractional Fourier optics. Opt. Eng. 35(3), 732-740 (1996) (Pubitemid 126664584)
    • (1996) Optical Engineering , vol.35 , Issue.3 , pp. 732-740
    • Bernardo, L.M.1
  • 7
    • 33749469804 scopus 로고    scopus 로고
    • Convolution theorems for the linear canonical transform and their applications
    • DOI 10.1007/s11432-006-2016-4
    • B. Deng, R. Tao, Y.Wang, Convolution theorems for the linear canonical transform and their applications. Sci. China Ser. F 49, 592-603 (2006) (Pubitemid 44521513)
    • (2006) Science in China, Series F: Information Sciences , vol.49 , Issue.5 , pp. 592-603
    • Deng, B.1    Tao, R.2    Wang, Y.3
  • 8
    • 57749196950 scopus 로고    scopus 로고
    • Sampling and discretization of the linear canonical transform
    • J.J. Healy, J.T. Sheridan, Sampling and discretization of the linear canonical transform. Signal Process. 89, 641-648 (2009)
    • (2009) Signal Process. , vol.89 , pp. 641-648
    • Healy, J.J.1    Sheridan, J.T.2
  • 9
    • 0030145797 scopus 로고    scopus 로고
    • The generalized Fresnel transform and its application to optics
    • D.F.V. James, G.S. Agarwal, The generalized Fresnel transform and its applications to optics. Opt. Commun. 126(5), 207-212 (1996) (Pubitemid 126369128)
    • (1996) Optics Communications , vol.126 , Issue.4-6 , pp. 207-212
    • James, D.F.V.1    Agarwal, G.S.2
  • 10
    • 33846571498 scopus 로고    scopus 로고
    • New sampling formulae related to linear canonical transform
    • DOI 10.1016/j.sigpro.2006.09.008, PII S0165168406003136
    • B.Z. Li, R. Tao, Y. Wang, New sampling formulae related to linear canonical transform. Signal Process. 87, 983-990 (2007) (Pubitemid 46186523)
    • (2007) Signal Processing , vol.87 , Issue.5 , pp. 983-990
    • Li, B.-Z.1    Tao, R.2    Wang, Y.3
  • 13
    • 36849112629 scopus 로고
    • Linear canonical transformations and their unitary representations
    • M. Moshinsky, C. Quesne, Linear canonical transformations and their unitary representations. J.Math. Phys. 12, 1772-1783 (1971)
    • (1971) J.Math. Phys. , vol.12 , pp. 1772-1783
    • Moshinsky, M.1    Quesne, C.2
  • 14
    • 0028382656 scopus 로고
    • Convolution, filtering, and multiplexing in fractional Fourier domains and their relationship to chirp and wavelet transforms
    • H.M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, Convolution, filtering, and multiplexing in fractional Fourier domains and their relationship to chirp and wavelet transforms. J. Opt. Soc. Am. A 11, 547-559 (1994)
    • (1994) J. Opt. Soc. Am. A , vol.11 , pp. 547-559
    • Ozaktas, H.M.1    Barshan, B.2    Mendlovic, D.3    Onural, L.4
  • 16
    • 0036173698 scopus 로고    scopus 로고
    • Eigenfunctions of linear canonical transform
    • S.C. Pei, J.J. Ding, Eigenfunctions of linear canonical transform. IEEE Trans. Signal Process. 50(1), 11-26 (2002)
    • (2002) IEEE Trans. Signal Process. , vol.50 , Issue.1 , pp. 11-26
    • Pei, S.C.1    Ding, J.J.2
  • 17
    • 77954564062 scopus 로고    scopus 로고
    • Sampling of bandlimited signals in fractional Fourier transform domain
    • Q.W. Ran, H. Zhao, L.Y. Tan, J. Ma, Sampling of bandlimited signals in fractional Fourier transform domain. Circuits Syst. Signal Process. 29, 459-467 (2010)
    • (2010) Circuits Syst. Signal Process. , vol.29 , pp. 459-467
    • Ran, Q.W.1    Zhao, H.2    Tan, L.Y.3    Ma, J.4
  • 18
    • 33748045831 scopus 로고    scopus 로고
    • Signal separation using linear canonical and fractional Fourier transforms
    • DOI 10.1016/j.optcom.2006.03.062, PII S003040180600321X
    • K.K. Sharma, S.D. Joshi, Signal separation using linear canonical and fractional Fourier transform. Opt. Commun. 265, 454-460 (2006) (Pubitemid 44302151)
    • (2006) Optics Communications , vol.265 , Issue.2 , pp. 454-460
    • Sharma, K.K.1    Joshi, S.D.2
  • 19
    • 46749112750 scopus 로고    scopus 로고
    • Uncertainty principle for real signals in the linear canonical transform domains
    • K.K. Sharma, S.D. Joshi, Uncertainty principle for real signals in the linear canonical transform domains. IEEE Trans. Signal Process. 56(7), 2677-2683 (2008)
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.7 , pp. 2677-2683
    • Sharma, K.K.1    Joshi, S.D.2
  • 20
    • 33646129911 scopus 로고    scopus 로고
    • Sampling of linear canonical transformed signals
    • A. Stern, Sampling of linear canonical transformed signals. Signal Process. 86, 1421-1425 (2006)
    • (2006) Signal Process. , vol.86 , pp. 1421-1425
    • Stern, A.1
  • 22
    • 76749102797 scopus 로고    scopus 로고
    • Fractional convolution, fractional correlation and their translation invariance properties
    • R. Torres, P. Pellat-Finet, Y. Torres, Fractional convolution, fractional correlation and their translation invariance properties. Signal Process. 90, 1976-1984 (2010)
    • (2010) Signal Process. , vol.90 , pp. 1976-1984
    • Torres, R.1    Pellat-Finet, P.2    Torres, Y.3
  • 23
    • 77952129659 scopus 로고    scopus 로고
    • A convolution and product theorem for the linear canonical transform
    • D.Y. Wei, Q.W. Ran, Y.M. Li, J. Ma, L.Y. Tan, A convolution and product theorem for the linear canonical transform. IEEE Signal Process. Lett. 16, 853-856 (2009)
    • (2009) IEEE Signal Process. Lett. , vol.16 , pp. 853-856
    • Wei, D.Y.1    Ran, Q.W.2    Li, Y.M.3    Ma, J.4    Tan, L.Y.5
  • 24
    • 77952173338 scopus 로고    scopus 로고
    • Generalized sampling expansion for bandlimited signals associated with the fractional Fourier transform
    • D.Y. Wei, Q.W. Ran, Y.M. Li, Generalized sampling expansion for bandlimited signals associated with the fractional Fourier transform. IEEE Signal Process. Lett. 17(6), 595-598 (2010)
    • (2010) IEEE Signal Process. Lett. , vol.17 , Issue.6 , pp. 595-598
    • Wei, D.Y.1    Ran, Q.W.2    Li, Y.M.3
  • 26
    • 0030107597 scopus 로고    scopus 로고
    • On bandlimited signals with fractional Fourier transform
    • X.G. Xia, On bandlimited signals with fractional Fourier transform. IEEE Signal Process. Lett. 3, 72-74 (1996)
    • (1996) IEEE Signal Process. Lett. , vol.3 , pp. 72-74
    • Xia, X.G.1
  • 27
    • 0032047886 scopus 로고    scopus 로고
    • A convolution and product theorem for the fractional Fourier transform
    • A.I. Zayed, A Product and convolution theorems for the fractional Fourier transform. IEEE Signal Process. Lett. 5, 101-103 (1998) (Pubitemid 128556806)
    • (1998) IEEE Signal Processing Letters , vol.5 , Issue.4 , pp. 101-103
    • Zayed, A.I.1
  • 28
    • 64249164703 scopus 로고    scopus 로고
    • On bandlimited signals associated with linear canonical transform
    • H. Zhao, Q.W. Ran, J. Ma, L.Y. Tan, On bandlimited signals associated with linear canonical transform. IEEE Signal Process. Lett. 16, 343-345 (2009)
    • (2009) IEEE Signal Process. Lett. , vol.16 , pp. 343-345
    • Zhao, H.1    Ran, Q.W.2    Ma, J.3    Tan, L.Y.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.