一种有效的10点DFT算法及其应用

Haijun Li, Ran Fei
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引用次数: 5

摘要

提出了一种计算10点DFT的高效算法,为求解更多n点DFT提供了快速算法。计算一个10点DFT只需要20次实乘法,84次实加法和4次实右移2位。根据时间抽取(DIT)或频率抽取(DIF)或双因子算法的原理以及10点DFT的高效算法,10M、10×M、2M×10、4M×10-point DFT分别有自己的高效算法。因此,许多n点dft都有自己的快速傅里叶变换算法。特别是在计算10点DFT的高效算法中,即在根数为10的FFT算法中,一个102点DFT需要720次实乘法、1840次实加法和80次实右移,一个103点DFT需要12760次实乘法、28580次实加法和1200次实右移2位,一个104点DFT需要183560次实乘法、387780次实加法和16000次实右移2位。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An Efficient Algorithm of 10-Point DFT and its Applications
An efficient algorithm for computing 10-point DFT, which can contribute fast algorithms to more N-point DFTs, is developed. The computation of one 10-point DFT requires only 20 real multiplications, 84 real additions and 4 real right-shiftings 2 bits. According to the principles of decimation-in-time (DIT) or decimation-in-frequency (DIF) or double factors algorithm and the efficient algorithm of 10-point DFT, 10M, 10×M, 2M×10, 4M×10-point DFT have their own efficient algorithms, respectively. Thus, many N-point DFTs are possessed of own fast fourier transform algorithms. Especially, in efficient algorithm for computing 10-point DFT, in other words, in radix-10 FFT algorithm, one 102-point DFT requires 720 real multiplications, 1840 real additions and 80 real right-shiftings, one 103-point DFT requires 12760 real multiplications, 28580 real additions and 1200 real right-shiftings 2 bits, and one 104-point DFT requires 183560 real multiplications, 387780 real additions and 16000 real right-shiftings 2 bits.
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