In this paper the authors present a new neural network model, called the constrained smallest l1-norm neural network (CSl1NN), for basis pursuit (BP) implementation. The BP is considered as a large-scale linear programming problem. In contrast with the simplex-BP or inferior-BP, the proposed CSl1NN-BP does not double the optimizing scale and can be implemented in real time via hardware. Using non-stationary artificial signals and electrogastrograms to test our simulations show that the CSl 1NN-BP presents an excellent convergence performance for a wide range of time-frequency (TF) dictionaries and has a higher joint TF resolution not only than the traditional Wigner distribution, but also other overcomplete representation methods. Combining the high resolution with the fast implementation, the CSl1NN-BP can be used for online time-frequency analysis of various kinds of non-stationary signals including medical data, such as ECG, EEG and EGG.