32-point DFT Approximations Based on Minimal Frobenius Error and DFT Symmetries

Abstract

This work introduces low-complexity, multiplierless approximations for the 32-point discrete Fourier transform. The proposed methods are obtained by minimizing the Frobenius error compared against the DFT matrix over a set of trivial multipliers. A row-wise, symmetry-constrained parameterization is employed to reduce the search space size, rendering the task computationally tractable. The resulting approximations could outperform the reference method in the literature according to energy-based error measurements. A sparse matrix factorization is provided for efficient computation; the arithmetic costs are 152 real additions and 34 bit-shifts only.