基于修正离散傅里叶变换的频域卷积混合盲分离

Frequency Domain Convolutive Blind Separation Based on Modified Discrete Fourier Transform

针对频域卷积混合盲分离,依据所导出的卷积混合信号每帧的频域表示模型,提出了一种最小均方误差意义下的最优变换——修正离散傅里叶变换,用于代替频域卷积混合盲分离中常用的离散傅里叶变换。在每个频率片上,卷积混合信号的修正离散傅里叶变换系数在最小均方误差意义下最接近于源信号频谱的瞬时混合。相对于离散傅里叶变换系数,现有瞬时混合盲分离算法能从修正离散傅里叶变换系数中更精确地估计各频率片上分离矩阵,从而提高现有频域卷积混合盲分离算法的分离性能。仿真结果证明了修正离散傅里叶变换对现有频域卷积混合盲分离算法的有效性。

Based on the derived frequency representation of each frame for convolutive mixtures, a modified discrete Fourier transform （MDFT） is proposed for the frequency domain convolutive blind separation. MDFT serves as an optimal transform in the minimum square error sense to replace the traditional DFT. On each frequency bin, MDFT coefficients approximate the instantaneous mixture of signal source spectrum in a minimum square error sense. The separation algorithm can estimate the separating matrix on each frequency bin from MDFT coefficients compared with DFT coefficients, thus improving the separation performance. Simulation results verify the validity of MDFT.