论文部分内容阅读
FFT 是按复数定义的,为了有效地利用复数点的虚部,文献[1]中已推导出用 N 点复数的 FFT 变换来计算实数2N 点的变换。在此基础上,我们详细推导出用 N 点复数的 FFT 变换来计算实数4N 点变换的算式,同时明确指出,此算式是通过复数变换来实现实数变换的最终公式。这种算法与变换4N点复数的虚部充零的 FFT 做法相比较,可以节约四分之三的内存单元;若以N=1024个实数点为例,乘法次数减少56.2％,加法次数减少50.0％。
FFTs are defined in terms of complex numbers. In order to effectively use the imaginary part of complex points, it has been derived in literature [1] to calculate the real 2N point transform using an N-point complex FFT transform. On this basis, we deduce in detail the N-point complex FFT transform to calculate the real 4N point transform algorithm, at the same time clearly pointed out that this formula is through the complex transform to achieve the real number transform the final formula. This algorithm can save about three-fourths of the memory cells compared with the FFT method of transforming the imaginary part of a 4N-point complex number. If N = 1024 real numbers are used, the number of multiplications is reduced by 56.2% and the number of additions is reduced by 50.0 %.