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为克服时频关系为线性的基函数的不足 ,提出了一种新的时频信号表示—— Dopplerlet变换。对其物理机制的分析表明 :该变换实质上是对信号的时频能量分布进行非线性分割 ,而以线性分割为特征的 Fourier变换、短时 Fourier变换 (包括 Gabor变换 )、小波变换、chirplet变换则均是Dopplerlet变换在其参数取特定值时的特例。采用自适应匹配投影分解法搜索出一组与信号分量最佳匹配的 Doppler-let基函数 ,据此可用尽可能少的波形重构原信号。文中还提出了时间和频率分辨率均达到理论值极限的“伪时频分布”的概念。
In order to overcome the shortcoming of time-frequency-based linear function, a new time-frequency signal representation-Dopplerlet transform is proposed. The analysis of its physical mechanism shows that the transform is essentially a nonlinear segmentation of the time-frequency energy distribution of the signal, while the Fourier transform, the short-time Fourier transform (including Gabor transform), the wavelet transform, the chirplet transform It is a special case of Dopplerlet transform when its parameter takes a certain value. Using adaptive matching projection method, a group of Doppler-let basis functions which are best matched with the signal components are found out, so that the original signal can be reconstructed with as few waveforms as possible. The paper also proposes the concept of “pseudo-time-frequency distribution” which both reaches the theoretical limit of time and frequency.