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Research Articles

A sampling theorem with error estimation for S-transform

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Pages 471-491 | Received 19 Jul 2018, Accepted 26 Feb 2019, Published online: 18 Mar 2019

References

  • Stockwell RG, Mansinha L, Lowe RP. Localization of the complex spectrum the S-transform. IEEE Trans Signal Process. 1996;44:998–1001. doi: 10.1109/78.492555
  • Assous S, Boashash B. Evaluation of the modified S-transform for time-frequency synchrony analysis and source localization. EURASIP J Adv Signal Process. 2012;49:1687–1680.
  • Stockwell RG. A basis for efficient representation of the S-transform. Digit Signal Process. 2007;17:371–393. doi: 10.1016/j.dsp.2006.04.006
  • Roopkumar R. Stockwell transform for boehmians. Integr Transf Spec Funct. 2012;24:251–262. doi: 10.1080/10652469.2012.686903
  • Ranjan R, Singh AK, Jindal N. Formulation of some useful theorem for S-transform. Optik – Int J Light Electron Opt. 2018;168:913–919. doi: 10.1016/j.ijleo.2018.05.009
  • Shi J, Xiang W, Liu X, et al. A sampling theorem for the fractional Fourier transform without band-limiting constraints. Signal Process. 2014;98:158–165. doi: 10.1016/j.sigpro.2013.11.026
  • Shi J, Tong ZN, Xiaoping L. A noval fractional wavelet transform and its applications. Sci China Inf Sci. 2012;55(6):1270–1279. doi: 10.1007/s11432-011-4320-x
  • Shi J, Liu X, He L, et al. Sampling and reconstruction in arbitrary measurement and approximation spaces associated with linear canonical transform. IEEE Trans Signal Process. 2016;64(24):6379–6391. doi: 10.1109/TSP.2016.2602808
  • Shi J, Sha X, Song X, et al. Generalized convolution theorem associated with fractional Fourier transform. Wirel Commun Mob Comput. 2014;14:1340–1351. doi: 10.1002/wcm.2254
  • Shi J, Chi Y, Zhang N. Multichannel sampling and reconstruction of bandlimited signals in fractional Fourier domain. IEEE Signal Process Lett. 2010;17(11):909–912. doi: 10.1109/LSP.2010.2071383
  • Shi J, Liu X, Sha X, et al. A sampling theorem for fractional wavelet transform with error estimates. IEEE Trans Signal Process. 2017;65(18):4797–4811. doi: 10.1109/TSP.2017.2715009
  • Shi J, Liu X, Yan FG, et al. Error analysis of reconstruction from linear canonical transform based sampling. IEEE Trans Signal Process. 2018;66(7):1748–1760.
  • Shi J, Liu X, Sha X, et al. Sampling and reconstruction of signals in function spaces associated with the linear canonical transform. IEEE Trans Signal Process. 2012;60(11):6041–6047. doi: 10.1109/TSP.2012.2210887
  • Akila L, Roopkumar R. Quaternionic stockwell transform. Integr Transf Spec Funct. 2016;27:484–504. doi: 10.1080/10652469.2016.1155570
  • Schimmel M, Gallart J. The inverse S-transform in filters with time-frequency localization. IEEE Trans Signal Process. 2005;53:4417–4422. doi: 10.1109/TSP.2005.857065
  • Pinnegar CR, Eaton DW. Application of the S-transform to prestack noise attenuation filtering. J Geophys Res Solid Earth. 2013;108:1–18.
  • Christensen O. Introduction to frames and Riesz bases. Boston (MA): Birkhauser; 2003.
  • Andrew A, Clark W, Nitzan S, et al. Density of Gabor systems via the short time Fourier transform. J Fourier Anal Appl. 2018;24:699–718. doi: 10.1007/s00041-017-9535-9
  • Casazza PG, Kakton O, Christensen NJ. Frame of translates. Collect Math. 2001;52(1):35–55.
  • Chen W, Ltoh S. A sampling theorem for shift-invariant subspace. IEEE Trans Signal Process. 1998;46(10):2822–2824. doi: 10.1109/78.720386
  • Aldroubi A, Grohenig K. Nonuniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 2001;43(4):585–620. doi: 10.1137/S0036144501386986
  • Zhuo ZH. Poission summation formulae associated with the special affine Fourier transform and offset Hilbert transform. Hindawi Math Prob Eng. 2017;2017:1–5.
  • Flandrin P. Time-frequency and chirps. Proc SPIE. 2001;4391:161–175. doi: 10.1117/12.421196
  • Pei SC, Ding JJ. Relations between fractional operations and time frequency distributions and their applications. IEEE Trans Signal Process. 2001;49(8):1638–1655. doi: 10.1109/78.934134
  • Unser M, Aldroubi A, Eden M. B-spline signal processing-part-1: theory. IEEE Trans Signal Process. 1993;41(2):821–833. doi: 10.1109/78.193220
  • Chui CK. An introduction to wavelets. Boston (MA): Academic Press; 1992.
  • Mathews JH, Howell RW. Complex analysis for mathematics and engineering. Boston (MA): Jones and Bartlett; 1997.

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