  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.
