Structures for evaluating the discrete Fourier transform on staggered blocks

In this work three structures are presented for evaluating in real time the discrete Fourier transform (DFT) on successive sections of a sampled signal. Each section consists of
N
elements and two successive sections are staggered of
M \leq N
elements. Each structure evaluates
N/M
DFT coefficients at every step and requires about
(N/(2M)) \log_{2} 4M
multipliers.