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On Convolution and Product Theorems for FRFT

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Abstract

The fractional Fourier transform (FRFT), which is considered as a generalization of the Fourier transform (FT), has emerged as a very efficient mathematical tool in signal processing for signals which are having time-dependent frequency component. Many properties of this transform are already known, but the generalization of convolution theorem of Fourier transform for FRFT is still not having a widely accepted closed form expression. In the recent past, different authors have tried to formulate convolution theorem for FRFT, but none have received acclamation because their definition do not generalize very appropriately the classical result for the FT. A modified convolution theorem for FRFT is proposed in this article which is compared with the existing ones and found to be a better and befitting proposition.

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References

  1. Namias V. (1980) The fractional Fourier transform and its application to quantum mechanics. Journal Institute of Mathematics and Applications 25: 241–265

    Article  MathSciNet  MATH  Google Scholar 

  2. Saxena R., Singh K. (2005) Fractional Fourier transform: A novel tool for signal processing. Journal Indian Institute of Science 85(1): 11–26

    Google Scholar 

  3. Almeida L. B. (1994) The fractional Fourier transform and time-frequency representations. IEEE Transactions of Signal Processing 42: 3084–3091

    Article  Google Scholar 

  4. Johnson, D. (2009). Efficiency of frequency-domain filtering. The connexions project and licensed under the Creative Commons Attribution License, June 11, 2009.

  5. Meng X. Y., Tao R., Wang Y. (2007) Fractional Fourier domain analysis of decimation and interpolation. Science in China Series F: Information Sciences 50(4): 521–538

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu S.-G., Fan H.-Y. (2009) Convolution theorem for the three-dimensional entangled fractional Fourier transformation deduced from the tripartite entangled state representation. Theoretical and Mathematical Physics 161(3): 1714–1722

    Article  MathSciNet  MATH  Google Scholar 

  7. Almeida L. B. (1997) Product and convolution theorems for the fractional Fourier transform. IEEE Signal Processing Letters 4(1): 15–17

    Article  MathSciNet  Google Scholar 

  8. Zayed A. I. (1998) A convolution and product theorem for the fractional Fourier transform. IEEE Signal Processing Letters 5(4): 101–103

    Article  MathSciNet  Google Scholar 

  9. Bing D., Ran T., Yue W. (2006) Convolution theorems for the linear canonical transform and their applications. Science in China Series F: Information Sciences 49(5): 592–603

    Article  MathSciNet  Google Scholar 

  10. Wei D., Ran Q., Li Y., Ma J., Tan L. (2009) A convolution and product theorem for the linear canonical transform. IEEE Signal Processing Letters 16(10): 853–856

    Article  Google Scholar 

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Correspondence to A. K. Singh.

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Singh, A.K., Saxena, R. On Convolution and Product Theorems for FRFT. Wireless Pers Commun 65, 189–201 (2012). https://doi.org/10.1007/s11277-011-0235-5

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  • DOI: https://doi.org/10.1007/s11277-011-0235-5

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