同时计算实序列的DFT和实序列的DFT的IDFT的新公式

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

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.

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.