Analytic derivation of the finite wordlength effect of the twiddle factors in recursive implementation of the sliding-DFT

Analytic derivation of the erroneous effect is presented for the sliding-DFT, which is implemented in a recursive way with the finite-bit approximation of the twiddle factors. The derivation is based on the statistical exploration of the error dynamic equation that describes the error propagation of the recursion. The analysis result is obtained in a closed-form equation of the noise-to-signal power ratio employing the zero-mean white Gaussian signal as the target input and is verified with the data obtained from the computer simulation.