Implicitly Dealiased Convolutions: Example Applications and Performance Comparison

Implicitly dealiasing is a recently-developed technique which improves upon conventional zero padding to compute linear convolutions via fast Fourier transforms. For onedimensional inputs, the memory requirements and performance are similar to conventional zero-padded convolutions, but implicitly dealiased convolutions are faster and require less memory when the data is multi-dimensional. We show how implicit dealiased convolutions can be used in some common applications and evaluate their performance using the FFTW++ library relative to the standard technique and in other implementations.