窗函数对信号稀疏特性的影响

Effect of Window Function on Signal's Sparse Characteristics

由于信号的稀疏特性有效地用于盲信号分离中,所以稀疏特性受到普遍的关注.本文对常见的几种窗函数与DFT以后频谱稀疏特性的关系进行了分析研究.提出了基于泄漏频带宽度和统计有效泄漏谱线数量的两个信号稀疏特性评判依据,并根据此评判依据研究了常见几种窗函数对信号稀疏特性的影响,选出使信号稀疏特性最佳的最优窗.分析结果表明,信号非整周期截取时汉宁窗可以获得最佳稀疏特性.研究结论可为基于时频域稀疏特性的信号分离方法或其它信号处理方法的研究提供一种技术支持.

The signal＇s sparse characteristic has got certain concern in recent years because of its usefulness in blind signal separation. The authors investigated the relations between the traditional window functions and the spectrum sparse characteristics after DFT, and put forward two sparse characteristicsr criterions based on the width of leakage spectrum frequency band and the number of effective spectrum lines. The influence of signal window functions on sparse characteristics on the basis of these two criterions is studied, and the optimal window function which can keep best sparse characteristic is selected. The analyzing results indicate that the Hanning window can get the best sparse characteristics in non-complete periodical interrupt. The conclusions can be expected to be a support in signal separation methods based on the sparse characteristics in time-frequency domain as well as other signal processing methods.