A new multidimensional FFT based on one-dimensional decompositions

This work proposes an original multidimensional fast Fourier transform (FFT) algorithm where the computation is first organized into multiplier-free butterflies and then completed by 1-D FFTs. The properties of well-known 1-D FFT algorithms blend in quite nicely with those of the proposed multidimensional FFT scheme, extending their computational and structural characteristics to it. Strong points of the proposed method are that its total computational cost decreases as the signal space dimensions increase and that its efficiency is superior to that of any other multidimensional FFT algorithm.