We introduce an efficient scheme for the construction of quadrature rules for bandlimited functions. While the scheme is predominantly based on well-known facts about prolate spheroidal wave functions of order zero, it has the asymptotic CPU time estimate $O(n log n)$ to construct an n-point quadrature rule. Moreover, the size of the ``$n log n$'' term in the CPU time estimate is small, so for all practical purposes the CPU time cost is proportional to $n$. The performance of the algorithm is illustrated by several numerical examples.

翻译：本文提出了一种高效方案，用于构造带限函数的求积法则。该方法主要基于零阶长椭球波函数的经典结论，其构造n点求积公式的渐进CPU时间估计为$O(n \log n)$。此外，CPU时间估计中“$n \log n$”项的系数较小，因此在所有实际应用中，CPU时间开销与$n$成正比。通过多个数值示例展示了该算法的性能。