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Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra

Year 2014, Volume: 2 Issue: 3, 233 - 241, 01.12.2014

Fariba Tattahi Mohsen Alimohammady

Abstract

This paper describes the moderateness of Short-time Fourier transform via the Caputo fractional derivative. Moreover, weconsider some properties of the generalized STFT in extended Colmbeau algebra

Keywords

Colombeau algebra STFT Caputo fractional derivative

References

  • J. F. Colombeau, New generalized functions and Multiplication of distributions, North-Holland, Amsterdam, 1984.
  • J. F. Colombeau and A. Y. L. Roux, Multiplications of distributions in elasticity and hydrodynamics, J. Math. Phys., 29 (1988), 315-319.
  • J. F. Colombeau, Elementary Introduction to New Generalized Functions, North-Holland Math. Studies Vol. 113, North-Holland, Amsterdam 1985.
  • J. ˘Sahbegovi ´c, Short-Time Fourier Transform and Modulation Spaces in Algebras of Generalized Functions , University of Vienna, (2009).
  • D. Rajter- ´Ciri ´c, M. Stojanovi ´c , Convolution type derivatives and transforms of Colombeau generalized stochastic processes, Integral Transforms and Special Functions, 22 (2011), 319-326.
  • M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations, Pitman Research Notes in Mathematics 259. Longman Scientific and Technical, 1992.
  • K. Grochenig.”Foundations of Time-Frequency Analysis”, Birkhauser, Boston, 2001.

Regularization Short-time Fourier transform in extended

Year 2014, Volume: 2 Issue: 3, 233 - 241, 01.12.2014

Fariba Tattahi Mohsen Alimohammady

Abstract

References

  • J. F. Colombeau, New generalized functions and Multiplication of distributions, North-Holland, Amsterdam, 1984.
  • J. F. Colombeau and A. Y. L. Roux, Multiplications of distributions in elasticity and hydrodynamics, J. Math. Phys., 29 (1988), 315-319.
  • J. F. Colombeau, Elementary Introduction to New Generalized Functions, North-Holland Math. Studies Vol. 113, North-Holland, Amsterdam 1985.
  • J. ˘Sahbegovi ´c, Short-Time Fourier Transform and Modulation Spaces in Algebras of Generalized Functions , University of Vienna, (2009).
  • D. Rajter- ´Ciri ´c, M. Stojanovi ´c , Convolution type derivatives and transforms of Colombeau generalized stochastic processes, Integral Transforms and Special Functions, 22 (2011), 319-326.
  • M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations, Pitman Research Notes in Mathematics 259. Longman Scientific and Technical, 1992.
  • K. Grochenig.”Foundations of Time-Frequency Analysis”, Birkhauser, Boston, 2001.
There are 7 citations in total.

Details

Journal Section Articles
Authors

Fariba Tattahi This is me

Mohsen Alimohammady This is me

Publication Date December 1, 2014
Published in Issue Year 2014 Volume: 2 Issue: 3

Cite

APA Tattahi, F., & Alimohammady, M. (2014). Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra. New Trends in Mathematical Sciences, 2(3), 233-241.
AMA Tattahi F, Alimohammady M. Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra. New Trends in Mathematical Sciences. December 2014;2(3):233-241.
Chicago Tattahi, Fariba, and Mohsen Alimohammady. “Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra”. New Trends in Mathematical Sciences 2, no. 3 (December 2014): 233-41.
EndNote Tattahi F, Alimohammady M (December 1, 2014) Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra. New Trends in Mathematical Sciences 2 3 233–241.
IEEE F. Tattahi and M. Alimohammady, “Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra”, New Trends in Mathematical Sciences, vol. 2, no. 3, pp. 233–241, 2014.
ISNAD Tattahi, Fariba - Alimohammady, Mohsen. “Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra”. New Trends in Mathematical Sciences 2/3 (December 2014), 233-241.
JAMA Tattahi F, Alimohammady M. Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra. New Trends in Mathematical Sciences. 2014;2:233–241.
MLA Tattahi, Fariba and Mohsen Alimohammady. “Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra”. New Trends in Mathematical Sciences, vol. 2, no. 3, 2014, pp. 233-41.
Vancouver Tattahi F, Alimohammady M. Regularization Short-Time Fourier Transform in Extended Colmbeau Algebra. New Trends in Mathematical Sciences. 2014;2(3):233-41.