On Cooley-Tukey FFT method for zero padded signals

The classical Cooley-Tukey fast Fourier transform (FFT) algorithm has the computational cost of O(Nlog
₂
N) 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(pNlog
₂
pN). This paper proposes an alternate instance of padding zeros to the data sequence that results in computational cost reduction to O(pNlog
₂
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