High-Speed Multidimensional Convolution

Fast computation algorithms are developed for twodimensional and general multidimensional convolutions. Two basic techniques (overlap-and-add, overlap-and-save) are described in detail. These techniques allow speed and storage requirement tradeoffs and they define a decomposition of the total convolution into partial convolutions that can be easily found by parallel use of fast sequential cyclic convolution algorithms. It is shown that unlike what is the case in one dimension, the ``overlap-and-save'' method enjoys a clear advantage over the ``overlap-and-add'' method with respect to speed and storage in multidimensional convolution. A specific computational burden is assessed for the case where these methods are used in conjunction with radix-2 fast Fourier transform algorithms.