This paper deals with the error analysis of the trapezoidal rule for the computation of Fourier type integrals, based on two double exponential transformations. The theory allows to construct algorithms in which the steplength and the number of nodes can be a priori selected. The analysis is also used to design an automatic integrator that can be employed without any knowledge of the function involved in the problem. Several numerical examples, which confirm the reliability of this strategy, are reported.

翻译：本文基于两种双指数变换，对用于计算傅里叶型积分的梯形法则进行了误差分析。该理论允许构造可先验选择步长与节点数的算法。该分析还被用于设计一种自动积分器，可在无需了解问题所涉及函数的情况下使用。文中还报告了若干数值算例，证实了该策略的可靠性。