In this paper, we consider a three-dimensional parameter space, which is the time-frequency-chirprate (TFCR), to characterize the time-varying features of multi-component non-stationary signals. By performing reassignment on the frequency-chirprate plane, a highly concentrated TFCR representation, named as the frequency-chirprate reassignment method (FCRM), is proposed. FCRM can provide the instantaneous frequency (IF) and chirprate (CR) estimates jointly, making the crossing of IFs appear as separated in the TFCR domain, which overcomes the limitation of the popular time-frequency post-processing methods that require input signal with non-overlapping IFs. Based on the chirplet transform, we derive the reassignment center of the FCRM, and a three-dimension ridge detection algorithm is introduced to extract the IFs and CRs from the FCRM. Numerical experiments demonstrate that the proposed FCRM provides a concentrated TFCR representation, obtaining a good IF estimation for the overlapped multi-component signals that contain cross-over IFs.

在本文中，我们考虑了三维参数空间，即时频chi（TFCR），以表征多分量非平稳信号的时变特征。通过在频率chi平面上进行重新分配，提出了一种高度集中的TFCR表示，称为频率representation重新分配方法（FCRM）。FCRM可以联合提供瞬时频率（IF）和线性调频（CR）估计，从而使IF的交叉在TFCR域中看起来像是分开的，从而克服了流行的时频后处理方法的局限性，即要求输入信号不带-重叠的IF。基于chirplet变换，我们推导了FCRM的重新分配中心，并引入了三维脊检测算法从FCRM中提取IF和CR。