  \emph{Multiresolution mode decomposition} (MMD) is an adaptive tool to
analyze a time series $f(t)=\sum_{k=1}^K f_k(t)$, where $f_k(t)$ is a
\emph{multiresolution intrinsic mode function} (MIMF) of the form
\begin{eqnarray*} f_k(t)&=&\sum_{n=-N/2}^{N/2-1} a_{n,k}\cos(2\pi
n\phi_k(t))s_{cn,k}(2\pi N_k\phi_k(t))\\&&+\sum_{n=-N/2}^{N/2-1}b_{n,k}
\sin(2\pi n\phi_k(t))s_{sn,k}(2\pi N_k\phi_k(t)) \end{eqnarray*} with
time-dependent amplitudes, frequencies, and waveforms. The multiresolution
expansion coefficients $\{a_{n,k}\}$, $\{b_{n,k}\}$, and the shape function
series $\{s_{cn,k}(t)\}$ and $\{s_{sn,k}(t)\}$ provide innovative features for
adaptive time series analysis. The MMD aims at identifying these MIMF's
(including their multiresolution expansion coefficients and shape functions
series) from their superposition. This paper proposes a fast algorithm for
solving the MMD problem based on recursive diffeomorphism-based spectral
analysis (RDSA). RDSA admits highly efficient numerical implementation via the
nonuniform fast Fourier transform (NUFFT); its convergence and accuracy can be
guaranteed theoretically. Numerical examples from synthetic data and natural
phenomena are given to demonstrate the efficiency of the proposed method.
