AI 中文总结
本研究提出低复杂度无乘法器的32点DFT近似方法，通过最小弗罗贝尼乌斯误差结合对称性约束缩小搜索空间，性能优于文献参考方法，算术成本仅含152次实数加法与34次移位，可高效计算。
AI 中文摘要
本研究针对32点离散傅里叶变换（DFT）提出了低复杂度、无乘法器的近似方法。该方法通过在一组平凡乘法器上最小化与DFT矩阵的弗罗贝尼乌斯误差得到，采用逐行、受对称性约束的参数化方式缩小搜索空间，使任务计算可行。基于能量的误差测量显示，所得近似方法性能优于文献中的参考方法；还提供了稀疏矩阵分解以实现高效计算，算术成本仅为152次实数加法和34次移位操作。
英文摘要
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.
Comments10 pages, 2 figures, 5 tables
