Three-dimension extracting transform

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. A highly concentrated TFCR representation, named as the three-dimension extracting transform (TET), is proposed based on instantaneous frequency (IF) and chirprate (CR) equations. The CRs and IFs can be jointly estimated via the TET, and the spectral clustering algorithm is applied for component separation. To avoid the influence of the CR parameter on the IF identification, a nonlinear exponential transform of the IF and CR equations is introduced. We further give a TET reconstruction with the theoretical analysis. By employing the TET, the signals crossing in the time-frequency domain can be well separated and robust IF estimation can be obtained. Numerical experiments on simulated signals demonstrate the effectiveness of the proposed approach.