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We consider the problem of the numerical evaluation of singular oscillatory Fourier transforms ∫abx-aαb-xβf(x)eiωxdx, whereα>-1 and β>-1. Based on substituting the original interval of integration by the paths of steepest descent, iffis analytic in the complex regionGcontaining [a,b], the computation of integrals can be transformed into the problems of integrating two integrals on [0, ∞) with the integrand that does not oscillate and decays exponentially fast, which can be efficiently computeddoi:10.1155/2014/984834 fatcat:klezqan2eras3kkpcswh6f5iba