Journal of computational and applied mathematics vol:43 pages:159-169
In this paper we consider a method for the computation of finite Fourier transforms of functions having endpoint singularities of algebraic or logarithmic type. This method may be considered as a modification of Clenshaw-Curtis quadrature. The nonoscillatory and nonsingular part of the integrand is replaced by a truncated Chebyshev series approximation and the integral is then evaluated using recurrence relations. The numerical stability of these recurrence relations is investigated.