  Signal decomposition and multiscale signal analysis provide many useful tools
for time-frequency analysis. We proposed a random feature method for analyzing
time-series data by constructing a sparse approximation to the spectrogram. The
randomization is both in the time window locations and the frequency sampling,
which lowers the overall sampling and computational cost. The sparsification of
the spectrogram leads to a sharp separation between time-frequency clusters
which makes it easier to identify intrinsic modes, and thus leads to a new
data-driven mode decomposition. The applications include signal representation,
outlier removal, and mode decomposition. On the benchmark tests, we show that
our approach outperforms other state-of-the-art decomposition methods.
