PreprintarXiv licencearXiv
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.
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BibTeX
@misc{andradesilva202632point,
title = {{32-point DFT Approximations Based on Minimal Frobenius Error and DFT Symmetries}},
author = {L. Andrade-Silva and W. A. S. Aleixo and R. J. Cintra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01115},
eprint = {2609.01115},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01115},
}
RIS
TY - UNPB
TI - 32-point DFT Approximations Based on Minimal Frobenius Error and DFT Symmetries
AU - L. Andrade-Silva
AU - W. A. S. Aleixo
AU - R. J. Cintra
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01115
UR - https://arxiv.org/abs/2609.01115
AB - 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.
ER -