同时计算实序列的DFT和实序列的DFT的IDFT的新公式

通过对离散傅里叶变换(DFT)的一些性质的分析，利用DFT的对称性和将一个复序列分解为4个奇偶序列之和的方法，改正了Gunther关于直接计算双实序列的DFT和实序列的DFT和逆离散傅里叶变换（IDFT）的公式中的少数错误，给出了新的同时计算实序列的DFT和实序列的DFT的IDFT的直接公式，并给出了证明.

The New Formulas of Simultaneously Calculating DFT of Real Sequence and IDFT of the DFT of Real Sequence

By analyzing some properties of discrete Fourier transform (DFT), exploiting the symmetries of DFT and decomposing a complex sequence into four sequences, a few mistakes in the direct formulas for simultaneously calculating the DFTs of two real sequences and the DFT & inverse discrete Fourier transform (IDFT) of real sequences which were proposed by Gunther were corrected, the new direct formulas of simultaneously calculating DFT of a real sequence and IDFT of the DFT of another real sequence were proposed and proved.