Reconstruction of locally frequency sparse nonstationary signals from random samples

The local sparsity property of frequency modulated (FM) signals stems from their instantaneous narrowband characteristics. This enables their reconstruction from few random signal observations over a short-time window. It is shown that for linear FM signals, the sparsity of the local frequencies is equal to the window length, thus adding another specification to the window selection requirements, beside the conventional temporal and spectral resolutions. Stable signal reconstruction within a sliding window depends on the underlying probability distribution function guiding the random sampling intervals. Both simulations and computational EM modeling data are used to demonstrate the effectiveness of local reconstructions. We consider both mono-component FM signals and multi-component signals, corresponding to maneuvering targets and human gait Doppler signatures, respectively.