A new multidimensional fast convolution algorithm

The article introduces a new fast convolution-type technique for computing the multidimensional periodic convolutions of signals defined on generic lattices. The method presented does not evaluate multidimensional periodic convolutions via multidimensional FFTs but with an original algorithm. The major advantages of this technique are that it is more efficient than the well-known FFT-based fast convolution method and that its efficiency increases with the signal's dimensionality. One striking indication of its computational efficiency is that the number of operations per output point required by this method with nonseparable kernels of assigned dimensions is always smaller than the number of operations required by classical fast convolution algorithms with separable kernels of identical dimensions.