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Fast discrete Pascal transform

Fast discrete Pascal transform

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© The Institution of Engineering and Technology
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An efficient structure for the fast computation of the discrete Pascal transform (DPT) is presented. Only ½N(N−1) additions are required for the computation of an N-point DPT as opposed to N2 multiplications and N(N−1) additions. The reduced computational complexity of the proposed algorithm results in significant time savings and software/hardware simplicity.

Inspec keywords: polynomial matrices; discrete transforms; computational complexity

Other keywords: computational complexity; N-point transform; fast discrete Pascal transform

Subjects: Linear algebra (numerical analysis); Integral transforms in numerical analysis; Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Integral transforms in numerical analysis; Computational complexity; Linear algebra (numerical analysis)

References

    1. 1)
    2. 2)
      • Goodman, T.J., Aburdene, M.F.: `Interpolation using the discrete Pascal transform', 2006 Conf. on Information Sciences and Systems, 22–24 March 2006, Princeton University, p. 1079–1083.
    3. 3)
      • Aburdene, M.F., Goodman, T.J.: `Discrete polynomials and filter design', Proc. 39th Conf. on Information Sciences and Systems, Paper #105, 16–18 March 2005, Baltimore, Maryland, The John Hopkins University, Session FA3 (Circuits).
    4. 4)
      • Wolfram Research, Mathworld: ‘Pascal's Triangle’ [on-line] http:// mathworld.wolfram.com/PascalsTriangle.html..
    5. 5)
      • Skodras, A.N.: `Efficient computation of the discrete Pascal transform', Proc. 14th European Signal Processing Conf. (EUSIPCO 2006), Sepember 2006, Florence, Italy.
    6. 6)
      • A. Edelman , G. Strang . Pascal matrices. Am. Math. Mon. , 3 , 189 - 197
    7. 7)
      • Goodman, T.J., Aburdene, M.F.: `A hardware implementation of the discrete Pascal transform for image processing', Proc. SPIE – S&T Electronic Imaging, 2006, 6064, SPIE, p. 60640H1–60640H8.
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