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Sampling Theorems for Fractional Laplace Transform of Functions of Compact Support

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IJCA Proceedings on International Conference on Benchmarks in Engineering Science and Technology 2012
© 2012 by IJCA Journal
ICBEST - Number 1
Year of Publication: 2012
Authors:
A. S. Gudadhe
P. R. Deshmukh

A S Gudadhe and P R Deshmukh. Article: Sampling Theorems for Fractional Laplace Transform of Functions of Compact Support. IJCA Proceedings on International Conference on Benchmarks in Engineering Science and Technology 2012 ICBEST(1):30-34, October 2012. Full text available. BibTeX

@article{key:article,
	author = {A. S. Gudadhe and P. R. Deshmukh},
	title = {Article: Sampling Theorems for Fractional Laplace Transform of Functions of Compact Support},
	journal = {IJCA Proceedings on International Conference on Benchmarks in Engineering Science and Technology 2012},
	year = {2012},
	volume = {ICBEST},
	number = {1},
	pages = {30-34},
	month = {October},
	note = {Full text available}
}

Abstract

Linear canonical transform is an integral transform with four parameters and has been proved to be powerful tool for optics, radar system analysis, filter design etc. Fractional Fourier transform and Fresnel transform can be seen as a special case of linear canonical transform with real parameters. Further generalization of linear canonical transform with complex parameters is also developed and Fractional Laplace transform is one of the special case of linear canonical transform with complex entities. Here we have studied the fractional Laplace transform of a periodic function of compact support. Newsamplingformulae for reconstruction of the functions that are of compact support in fractional Laplace transform domain have been proposed. More specifically it is shown that only (2k+1) coefficients are sufficient to construct any fractional Laplace transform domain of periodic function with compact support,where k is the order of positive highest nonzero harmonic component in the ?^th domain.

References

  • Brown J. L. : Sampling band limited periodic signals-An application to Discrete Fourier transform, Jr. IEEE tra. Edu. E-23(1980), pp. 205.
  • Deshmukh P. R. , Gudadhe A. S. : Analytical study of a special case of complex canonical transform. Global journal of mathematical sciences (T&P), Vol. 2, (2010), 261-270.
  • Deshmukh P. R. , Gudadhe A. S. : Convolution structure for two version of fractional Laplace transform. Journal of science and arts, No. 2 (15), (2011), 143-150.
  • Ozaktas H. M. , Zalevsky Z. , Kutay M. A. : The fractional Fourier transform with applications in optics and signal processing, Wiley Chichester, 2001.
  • Pei S. C. , Ding J. J. : Eigen functions of linear canonical transform. IEEE tran. On signal processing, vol. 50, no. 1, Jan. 2002.
  • Sharma K. K. , Joshi S. D. : Fractional Fourier transform of band limited periodic signal and its sampling theorems. Optics Communication 256 (2005), 272-278.
  • Stern A: Sampling of linear canonical transformed signals, Signal processing 86(7), (2006), 1421-1425.
  • Torre A. : Linear and radial canonical transforms of fractional order. Computational and App. Math. 153, 2003, 477-486.
  • Xia X: On band limited signal Fractional Fourier transform, IEEE Sig. Proc. Let. 3 (1996) 72.
  • Zayed A. I. , Garcia A. G. : New sampling formulae for the fractional Fourier transform. Signal pro. 77 (1999), 111-114.