On Cooley-Tukey FFT method for zero padded signals

Abstract

The classical Cooley-Tukey fast Fourier transform (FFT) algorithm has the computational cost of O(Nlog2N) where N is the length of the discrete signal. Spectrum resolution is improved through padding zeros at the tail of the discrete signal, if (p -1)N zeros are padded (where p is an integer) at the tail of the data sequence, the computational cost through FFT becomes O(pNlog2pN). This paper proposes an alternate instance of padding zeros to the data sequence that results in computational cost reduction to O(pNlog2 N). It has been noted that this modification can be used to achieve non-uniform upsampling that would zoom-in or zoom-out a particular frequency band, in addition, it may be used for pruning the spectrum, which would reduce resolution of an unimportant frequency band