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This paper develops new theory and algorithms for 1D general modedecompositions. First, we introduce the 1D synchrosqueezed wave packettransform and prove that it is able to estimate the instantaneous informationof well-separated modes from their superposition accurately. Thesynchrosqueezed wave packet transform has a better resolution than thesynchrosqueezed wavelet transform in the time-frequency domain for separatinghigh frequency modes. Second, we present a new approach based ondiffeomorphisms for the spectral analysis of general shape functions. These twomethods lead to a framework for general mode decompositions under a weakwell-separation condition and a well different condition. Numerical examples ofsynthetic and real data are provided to demonstrate the fruitful applicationsof these methods.

Synchrosqueezed Wave Packet Transforms and Diffeomorphism Based Spectral Analysis for 1D General Mode Decompositions