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Unification of Legendre, Laguerre, Hermite, and binomial discrete transforms using Pascal's matrix

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Abstract

Pascal's matrix plays an important role in the computation of the discrete Legendre, Laguerre, Hermite, and binomial transforms. In particular, Pascal's matrix helps to unify the formulation of these orthogonal transforms and demonstrate the similarity of the computation of the transform matrices. It also allows the identification of the identical computations needed for these transforms. The fundamental finding is based on the discovery of the relationship between Pascal's matrix and the binomial coefficient.

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Authors and Affiliations

  1. Department of Electrical Engineering, Bucknell University, 17837, Lewisburg, PA

    Maurice F. Aburdene

  2. NASA/Goddard Space Flight Center, 20771, Greenbelt, MD

    John E. Dorband

Authors
  1. Maurice F. Aburdene
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  2. John E. Dorband
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Aburdene, M.F., Dorband, J.E. Unification of Legendre, Laguerre, Hermite, and binomial discrete transforms using Pascal's matrix. Multidim Syst Sign Process 5, 301–305 (1994). https://doi.org/10.1007/BF00980712

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  • DOI: https://doi.org/10.1007/BF00980712

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