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被开发。描述了一种混合方法，该方法结合了显式去混叠（显式地将输入数据补零）和隐式去混叠（在数学上考虑这些零值）的传统实践。新方法将隐式去混叠推广到任意补零比率，并将显式去混叠作为其特例。与现有隐式去混叠实现不同，混合去混叠根据卷积几何结构定制其子变换尺寸。通过将多维卷积分解为低维卷积，实现了多维卷积的混合去混叠。通过伪代码说明了等长复值输入和埃尔米特输入的卷积，并在开源FFT++库中实现。混合去混叠在一维、二维和三维中均展现出优于显式去混叠的性能。