This paper addresses the analysis of the time-frequency technique so-called the second-order synchrosqueezing transform derived from continuous wavelet transform of multicomponent AM-FM signals. Such a technique is designed to deal with the signals consisting of strong frequency modulation components or modes. Before going into the details of this analysis, we revisit the case where the modes are assumed to be with weak frequency modulation as in the seminal paper of Daubechies et al. [1], but not assuming the wavelet is compactly supported in the Fourier domain. The remainder of the paper is devoted to the theoretical analysis of the second order wavelet-based syn-chrosqueezing transform [2] and we then put forward its differences compared with variants of the proposed technique. Numerical simulations assessing and comparing the quality of the different synchrosqueezing operators conclude the paper.