The practical applications of the digital convolution and of the discrete Fourier transform (DFT) have gained growing importance over the last few years. This is a direct consequence of the major role played by digital filtering and DFTs in digital signal processing and by the increasing use of digital signal processing techniques made possible by the rapidly declining cost of digital hardware. The motivation for developing fast convolution and DFT algorithms is strongly rooted in the fact that the direct computation of length-N convolutions and DFTs requires a number of operations proportional to N2 which becomes rapidly excessive for long dimensions. This, in turn, implies an excessively large requirement for computer implementation of the methods.
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