A novel approach for the computation of Legendre polynomial expansions
Neal C. Gallagher, G.L. Wise, John Burton Allen · IEEE Transactions on Acoustics Speech and Signal Processing · 1978
In this paper we present a novel technique for the computation of Legendre polynomial expansions. Given a function H(x) to be expanded in a polynomial series, we first use the fast Fourier transform (FFT) to compute a vector of Fourier coefficients. Then, using a change of basis transformation, we go from the Fourier coefficients to the polynomial coefficients. We investigate convergence properties for this new approach.