有限数据下循环谱的频域平滑对称式周期图法估计性能分析

Performance Estimation for Cyclic Spectrum by Frequency-Smoothing Symmetrical Periodogram Based on Limited Data Length

研究了循环谱在短时信号处理中的应用问题 ,推导了在有限数据条件下 ,循环谱的对称式周期图估计和频域平滑对称式周期图估计的估计方差表达式 ,并从平滑估计后的分辨率与方差两方面 ,分析了循环谱的频域平滑对称式周期图法估计性能 ,得出了存在最佳平滑点数以及频域平滑循环谱估计是渐进一致估计的结论。最后用计算机模拟的实例验证了结论的正确性。

The application of the cyclic spectrum to short-time signal processing is discussed. The variances expression of the estimation for the cyclic spectrum is deduced by the symmertical periodogram and the frequency-smoothing symmetrical periodogram. The estimation performance is analyzed for the cyclic spectrum by the frequency-smoothing symmetrical periodogram from the resolution and the variance in the case of limited data length. It is deduced that there exists the best smoothing point and the frequency-smoothing estimation for the clylic seectrum is asymptotically consitent. Finally,computer simulation is in agreement with the analytial results.