For nonstationary time series i.e. natural electromagnetic field and acoustical signal, effective signal extraction always requires prior knowledge or hypothesis, and hardly do without artificial judgment. We proposed bat algorithm sparse decomposition (BASD) to realize adaptive recognition and extraction of nonstationary signal in a noisy background. We designed two general atomics for typical signals, and developed dictionary training method based on correlation detection and Hilbert transform. The sparse decomposition was turned into an optimizing problem by introducing bat algorithm with optimized fitness function. By contrast with variational modal decomposition, it was indicated that BASD can effectively extract short time target without inducing global aliasing of local feature, and no preset mode number and late screening were needed.