窗长对于时频域盲源分离算法影响的实验分析

Experimental Analysis of the Influence of Window Length on Time-frequency Domain Blind Source Separation Algorithms

大多数盲源分离算法利用窄带假设将时域卷积混合模型近似为时频域瞬时混合模型,比如知名的独立成分分析、独立向量分析和独立低秩矩阵分析算法,但是这种近似会引入误差。近似误差与短时傅里叶变换分析窗的长度有关,所以短时傅里叶变换分析窗的长度会影响这类算法的性能。现有研究对短时傅里叶变换分析窗的长度关注较少,并且这些研究采用的信号长度均比较短。我们探究了短时傅里叶变换分析窗的长度和混合信号长度对于独立向量分析和独立低秩矩阵分析算法性能的影响。相比于现有研究指出的最优分析窗的长度由信号长度和混响时间共同决定的结论,发现:当信号长度较短时,最优分析窗的长度小于混响时间;当信号长度较长时,最优分析窗的长度大于混响时间。此外,我们展示了算法性能与混合信号长度的关系:当短时傅里叶变换分析窗的长度固定时,随着混合信号长度的增加,算法的分离性能会逐渐变好并趋于稳定。窗长越长,算法在混合信号长度较短时取得的性能越差,在混合信号长度越长时取得的性能越好。

Most blind source separation algorithms utilize the narrowband assumption to approximate the time-domain convolutional mixing model as the time-frequency domain instantaneous mixing model,such as independent component analysis,independent vector analysis(IVA),and independent low-rank matrix analysis(ILRMA).The accuracy of the approximation is related to the window length of the short-term Fourier transform(STFT),and hence the STFT window length has an impact on the performance of these algorithms.Only a few studies paid attention to the STFT window length,where the mixtures are usually rather short.In this paper,we investigate the effect of the STFT window length and signal length on the performance of IVA and ILRMA.Compared with the existing research result that the optimal STFT window length is determined by the trade-off between the reverberation time and signal length,we find that:when the mixture is short,the optimal STFT window is shorter than the reverberation time;when the mixture is long,the optimal STFT window is longer than the reverberation time.We show the relationship between the performance and signal length:when the STFT window length is fixed,the performance is gradually improved and tends to be stable as the signal length increases;the longer the window length,the worse the performance using short signal lengths,and the better performance using long signal lengths.