Abstract: Recent years,Compressed Sensing is one of the most popular technology in signal processing fields.However,the traditional theory of CS leaves certain structure of sparse signals out of consideration,such as,block sparse.Aimed at multi-band block sparse streaming signals in compressed sensing,we combined sparse signals’ reconstitution algorithm and modulating Discrete Prolate Spheroidal Sequence(DPSS) to establish the multi-band block sparse model.Then we use the correlations between the signals of two continuous windows to model the process in the state-space form so the original signals can be regained with Kalman filter.Compared with Fourier_based,DPSS_based reduces the complexity of sampled structure and settles spectrum leakage.The simulation reveals that multi_band signals can achieve much better restorability in DPSS basis than Fourier basis.