Recursive Computation of Discrete Legendre Polynomial Coefficients

摘要

Discrete Legendre polynomials play an important role in image processing, signal processing, and control. This paper presents two new recursive methods to compute Legendre polynomials' coefficients. One method computes the coefficients of the (m + 1 )th order term using the coefficient of the mth order term of the same degreee plynomial. The other method computes the nth order coefficient of a higher degree polynomial using the mth order coefficient of a lower degree polynomial.