The paper enhances the accuracy of the one-dimensional fractional Fourier transform (FRFT) using the closed Newton Cotes quadrature rules. Given the weights generated by the Composite Newton Cotes rules of order QN, it is shown that a FRFT of a QN-long weighted sequence can be written as two composites of FRFTs. The first composite of FRFTs is made up of a FRFT of a Q-long weighted sequence and a FRFT of a N-long sequence. The second composite is made up of a FRFT of a N-long weighted sequence and a FRFT of a Q-long sequence. The Empirical evidence suggests that the composite FRFTs has commutative property and works both algebraically and numerically. The composite of FRFTs is applied to the problem of inverting Fourier and Laplace transforms. The results show that the composite FRFTs outperforms both the simple non-weighted FRFT and the Newton-Cotes integration method, but the difference is less significant for the integration method.

翻译：本文采用闭牛顿-科特斯求积法则提高一维分数阶傅里叶变换（FRFT）的精度。基于QN阶复合牛顿-科特斯法则生成的权重，证明了长度为QN的加权序列的FRFT可表示为两个FRFT复合运算形式。第一个复合FRFT由长度为Q的加权序列的FRFT与长度为N的序列的FRFT组成；第二个复合FRFT则由长度为N的加权序列的FRFT与长度为Q的序列的FRFT构成。经验证据表明，该复合FRFT具有交换性质，且在代数和数值层面均有效。将复合FRFT应用于傅里叶变换和拉普拉斯变换的逆变换问题，结果显示：复合FRFT的性能优于简单非加权FRFT和牛顿-科特斯积分法，但与积分法的性能差异较小。