基于FRFT的改进多尺度线调频基稀疏信号分解方法

Improved multi-scale chirplet sparse signal decomposition method based on Fractional Fourier Transform

针对全局搜索基函数计算量大的问题,提出了基于分数阶傅里叶变换(Fractional Fourier Transform,FR-FT)确定基函数的改进多尺度线调频基稀疏信号分解方法。通过解析信号的FRFT消除实信号FRFT结果中的对称项,两级搜索FRFT幅度谱确定信号的最佳基函数,检验该方法的计算效率和抗噪性能,并采用该方法分解频率呈曲线变化的多分量非平稳信号。试验结果表明:对解析信号进行FRFT能有效消除实信号FRFT结果中的对称项;基于FRFT确定基函数速度快、精度高、抗噪能力强,与频偏大小、频率变化快慢无关,不需先验知识,有效克服了全局搜索方法计算量过大的问题;基于FRFT的改进多尺度线调频基稀疏信号分解方法能快速、准确地分解频率呈曲线变化的多分量信号,适合于旋转机械瞬变工况下非平稳信号的瞬时频率估计与目标分量隔离分析。

In view of the large computation of the global searching algorithm of basic function, an improved multi-scale chirplet sparse signal decomposition method （IMSCSD） is proposed in which the basic function is ascertained by Fractional Fourier Transform （FRFT）. The symmetric items of real signal＇s FRFT are removed by the FRFT of the analytic signal, and the FR- FT amplitude spectrum is searched by two-step peak searching method to ascertain the best basic function. The efficiency and anti noise performance of the IMSCSD is checked up, and IMSOSD is applied to decompose the non-stationary signal with multi-components whose frequencies change curvedly. The results show that the symmetry items of the FRFT of real signal is removed effectively by the FRFT of corresponding analytic signal; the basic function is ascertained by FRFT rapidly, precisely and robustly without the help of experience, and the method has no relation to frequency offset and frequency changing rate, so the large computation of global searching algorithm is overcome effectively; the signal with multi-components whose frequen- cies change curvedly is decomposed fast and precisely by IMSCSD, so the IMSCSD is very suitable for the evaluation of instantaneous frequencies and separation of targeted component of the non-stationary signal of rotational machine under transient condition.