Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We propose a signal representation algorithm using a sparse and randomized short-time Fourier transform. This builds from the recent sparse random feature expansion for approximating high-dimensional functions. The randomization is both in the time window location and the frequency sampling, which lowers the overall sampling and computational cost. Sparse optimization extracts a sparse time-frequency representation, which has the added benefit of forming a simple decomposition due to the sharpening of the spectrograph. Experiments on synthetic data show that the decomposition closely resembles the multiscale properties of the data and tests on real datasets show robustness. Comparisons show that our proposed approach performs better or is comparable to other state-of-the-art or popular methods.

This is joint work with Nicholas Richardson (UWaterloo), Hayden Schaeffer (CMU), and Rachel Ward (UTAustin).