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本文提出了一个N_1×N_2×…×N_n点组N维离散傅里叶变换的有效高速算法。该算法要求个复数加法和个复数乘法。从本文中,可以看到多维快速傅里叶算法的数据组织和具体算法与一维快速傅里叶算法的数据组织和具体算法与一维快速傅里叶算法是一样的。由于计算结果仍放在原始数据的相应位置,因此,用这样的代换算法,其存储量的要求,只限于原始数据的存储量即可。
In this paper, we propose an efficient high-speed algorithm for the N-dimensional discrete Fourier transform of N_1 × N_2 × ... × N_n points. The algorithm requires complex additions and complex multiplications. From this paper, we can see that the data organization and the specific algorithm of the multi-dimensional fast Fourier algorithm are the same as those of the one-dimensional fast Fourier algorithm and the specific algorithms are the same as the one-dimensional fast Fourier algorithm. Since the calculation result is still placed on the corresponding position of the original data, the storage requirement of this substitution algorithm is only limited to the storage of the original data.