Efficient algorithms for computing linear convolutions based on the fast Fourier transform are developed. A hybrid approach is described that combines the conventional practice of explicit dealiasing (explicitly padding the input data with zeros) and implicit dealiasing (mathematically accounting for these zero values). The new approach generalizes implicit dealiasing to arbitrary padding ratios and includes explicit dealiasing as a special case. Unlike existing implementations of implicit dealiasing, hybrid dealiasing tailors its subtransform sizes to the convolution geometry. Multidimensional convolutions are implemented with hybrid dealiasing by decomposing them into lower-dimensional convolutions. Convolutions of complex-valued and Hermitian inputs of equal length are illustrated with pseudocode and implemented in the open-source FFTW++ library. Hybrid dealiasing is shown to outperform explicit dealiasing in one, two, and three dimensions.

翻译：基于快速傅里叶变换的高效线性卷积算法得以发展。本文描述了一种混合方法，它结合了显式反折叠（在输入数据末尾显式补零）与隐式反折叠（通过数学处理这些零值）的常规实践。该新方法将隐式反折叠推广至任意填充比例，并将显式反折叠作为其特例。与现有隐式反折叠实现不同，混合反折叠可根据卷积几何结构调整其子变换尺寸。通过将多维卷积分解为低维卷积，混合反折叠实现了多维卷积处理。文中以伪代码形式展示了等长复数值及厄米共轭输入信号的卷积运算，并在开源库FFTW++中完成实现。实验表明，混合反折叠在一维、二维及三维场景中的性能均优于显式反折叠方法。