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A VLSI architecture for the real time computation of discrete trigonometric transforms

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Abstract

The Discrete Trigonometric Transforms are defined as a class of transforms. An algorithm for calculating the Discrete Fourier Transform is extended to cover all members of the defined class. A VLSI architecture which provides for real time calculation of these transforms is presented. This architecture provides simple interconnections, identical processing elements and minimal control complexity.

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References

  1. J.W. Cooley and J.W. Tukey, “An algorithm for the machine calculation of complex Fourier series,”Math. Computation, vol. 19, 1965, pp. 297–301.

    Article  MathSciNet  MATH  Google Scholar 

  2. J.W. Cooley, P.A.W. Lewis and P.D. Welch, “Historical notes on the fast Fourier transform,”IEEE Trans. Audio Electroacoust., vol. AU-15, 1967, pp. 76–69.

    Article  Google Scholar 

  3. R.C. Singleton, “A method for computing the fast Fourier transform with auxiliary memory and limited high speed storage,”IEEE Trans. Audio Electroacoust., vol. AU-17, 1967, pp. 91–98.

    Article  Google Scholar 

  4. R.C. Singleton, “An algorithm for computing the mixed radix fast Fourier transform,”IEEE Trans. Audio Electroacoust., vol. AU-17, 1967, pp. 93–103.

    Google Scholar 

  5. J.A. Beraldin, T. Aboulnasr and W. Steenhart, “Efficient one-dimensional systolic array realization of the discrete Fourier transform,”IEEE Transactions on Circuits and Systems, vol. 36, 1989, pp. 95–100.

    Article  Google Scholar 

  6. J.A. Beraldin and W. Steenhart, “Overflow analysis of a fixed-point implementation of the Goertzel algorithm,”IEEE Transactions on Circuits and Systems, vol. 36, 1989, pp. 322–324.

    Article  Google Scholar 

  7. J.A. Beraldin, “VLSI systolic array architecture for the computation of the discrete Fourier transform,” M.A.Sc. thesis, University of Ottawa, Canada, 1986.

    Google Scholar 

  8. G. Goertzel, “An algorithm for the evaluation of finite trigonometric series,”Amer. Math. Monthly, vol. 65, 1958, pp. 34–35.

    Article  MathSciNet  MATH  Google Scholar 

  9. B. Gold and C. Rader,Digital Processing of Signals, New York: McGraw-Hill, 1969.

    MATH  Google Scholar 

  10. A. Oppenheim and R. Schafer,Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1975.

    MATH  Google Scholar 

  11. N. Ahmed, T. Natarajan and K.R. Rao, “Discrete cosine transform,”IEEE Transactions on Computers, 1974, pp. 90–93.

  12. A.K. Jain, “A fast Karhunen Loeve transform for a class of stochastic processes,”IEEE Trans. Commun., vol. COM-24, 1976, pp. 1023–1029.

    Article  Google Scholar 

  13. R.N. Bracewell, “Discrete Hartley transform,”J. Opt. Soc. Amer., vol. 73, 1983, pp. 1832–1835.

    Article  Google Scholar 

  14. J. Canaris, “A VLSI architecture for the real time computation of discrete trigonometric transforms,” MSEE thesis, University of Idaho, Moscow; Idaho, 1990.

    Google Scholar 

  15. B.A. Bowen and W.R. Brown,Systems Design, Volume II of VLSI Systems Design for Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1985.

    Google Scholar 

  16. S.Y. Kung, H.J. Whitehouse and T. Kailath (Eds.),VLSI and Mod-ern Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1985.

    Google Scholar 

  17. J. Canaris, “A high speed fixed point binary divider,”The Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, 1989, pp. 2393–2396.

    Article  Google Scholar 

  18. Plessey Semiconductors,” “PDSP16256/A programmable FIR filter,” Product Description, Publication No. PS2330, March 1990.

  19. K. Cameron, S. Whitaker and J. Canaris, “ACE: Automatic centroid extractor for real time target tracking,”The Proceedings of the Second Annual NASA Space Engineering Research Center Symposium on VLSI Design, 1990, pp. 8.2.1–8.2.8.

  20. J. Ullman,Computational Aspect of VLSI, Rockville, MD: Computer Science Press, 1984.

    Google Scholar 

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Canaris, J. A VLSI architecture for the real time computation of discrete trigonometric transforms. J VLSI Sign Process Syst Sign Image Video Technol 5, 95–104 (1993). https://doi.org/10.1007/BF01880275

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  • DOI: https://doi.org/10.1007/BF01880275

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