调频初相位补偿的广义Warblet变换时频分析

信号时频分析的长时间窗时频分析法通常可提高输出信噪比和频率分辨率，但对于调频信号，会降低线谱时频能量聚集度并影响瞬时频率估计。对于调频信号广义Warblet变换(Generalized Warblet Transform,GWT)，具有较短时傅里叶变换(Short Time Fourier Transform,STFT)更优的时频分析性能，但在长时间窗分析时，调频初相位估计误差会使算法性能下降甚至失效。针对该问题，提出调频初相位补偿的GWT(Frequency Modulation Initial Phase CompensationGWT,FMIPC-GWT)时频分析方法。在调频参数估计时将一半时间窗长所经过的相位补偿到调频初相位中，提高调频参数估计的准确性以增加瞬时频率估计精度。仿真和实验数据验证了，相比STFT法和GWT法，FMIPC-GWT法对于非线性调频信号时频分析性能更优。FMIPC-GWT法在调频信号线谱检测与瞬时频率估计等方面具有应用前景。

Generalized Warblet transform method for time-frequency analysis with frequency modulation initial phase compensation

In signal time-frequency analysis, the long-time window analysis often improves the output signal-to-noise ratio and frequency resolution. However, for frequency modulation signals, the time-frequency energy concentration of the line spectrum can be reduced to affect the instantaneous frequency estimation. The generalized Warblet transform (GWT) method has a better time-frequency analysis performance than the short time Fourier transform (STFT) for frequency modulation signals, but the performance degrades or even fail in long time window analysis because of the estimation errors of the frequency modulation initial phases. To solve this problem, a time-frequency analysis method of GWT with frequency modulation initial phase compensation (FMIPC-GWT) is proposed. During the frequency modulation parameter estimation, the phase passed by half of the time window is compensated to the initial phase of the modulation components, and the accuracy of the parameter estimation is improved to make the instantaneous frequency estimation more accurate. The simulation and experimental data verify that this method has a better performance for nonlinear frequency modulation signals than the STFT and GWT methods. FMIPC-GWT method has a promising application in the line spectrum detection and instantaneous frequency estimation for frequency modulation signals.