  This paper develops new theory and algorithms for 1D general mode
decompositions. First, we introduce the 1D synchrosqueezed wave packet
transform and prove that it is able to estimate the instantaneous information
of well-separated modes from their superposition accurately. The
synchrosqueezed wave packet transform has a better resolution than the
synchrosqueezed wavelet transform in the time-frequency domain for separating
high frequency modes. Second, we present a new approach based on
diffeomorphisms for the spectral analysis of general shape functions. These two
methods lead to a framework for general mode decompositions under a weak
well-separation condition and a well different condition. Numerical examples of
synthetic and real data are provided to demonstrate the fruitful applications
of these methods.
