A simple design for a fast sliding DFT computer

In this paper, we present a simple design of a fast sliding DFT computer. This computer is a cascade of a comb filter section and a modification of the complex version of the Goertzel algorithm. This modification allows for the computation of the N-point DFT in N iterations. The algorithm has the flexibility of computing any portion of the transform domain with arbitrary resolution. The problem of multiplication by the complex coefficient
\exp (j2\pik/N)
is resolved using a cascade of rotation operators. The smallest rotation of 2π/N is realized using either a dedicated hardware structure or a software routine. In either method, the approximations
\sin(2\pi/N\simeqq/2^{m}
and
\cos(2\pi/N)\simeq1 - (q/2^{m})^{2}/2
lead to a very economical implementation. The representation of the exponent k using generalized canonical signed-digit code leads to a minimum number of required rotation operations. The overall efficiency is comparable to that of the FFT when a sliding type of operation is used.