Dopplerlet变换及其匹配收敛性分析

DOPPLERLET TRANSFORM AND ANALYSIS OF ITS MATCHING CONVERGENCE

介绍了一种以伸缩、时移和频移后的加窗Doppler信号为基函数的时频信号表示—Dopplerlet变换,证明了基于Dopplerlet基函数的自适应匹配投影塔形分解算法是收敛的,而且分解过程中所得残差信号的能量按指数律衰减。实验结果表明了以Dopplerlet为基函数的自适应匹配投影塔形分解法能更紧凑地表示自然界中的一类Doppler信号。

A new time-frequency representation called Dopplerlet transform, which uses the dilated, translated and moduiated windowed Doppler signals as its basis functions, is introduced. It is proved that the matchihg pursuits based on Dopplerlet basis functions are convergent, and that the energy of residual signals yielded in the decomposition process decays exponentially. Simulation results show that the matching pursuits with Dopplerlet basis functions can char-acterize compactly a nonstationary signal.