The authors present a new optimization neural network, which can be called as constrained smallest l1-norm neural network (CSl1NN), to implement the Basis Pursuit(BP)[1][2][3]for high resolution time-frequency analysis. As the new and generalized one of the communities of overcomplete signal representations, the BP is considered as a large-scale linear programming problem. In contrast with the Simplex-BP or Interior-BP in [2],the proposed CSl1NN-BP dose not double the optimizing scale and can be implemented in real time through hardware. Taking non-stationary artificial signals and Electrogastrograms (EGGs) to test, our simulations show that the CSl1 NN 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 (WD), but also than recently rising other overcomplete representation methods, such as Method of Frames (MOF)[9], Best Orthogonal Basis (BOB)[10] and Matching Pursuit (MP)[4]. Combining the high resolution with the fast implementation,the CSl1NN-BP will be very promising for on-line time frequency analysis of various kinds of non-stationary signals,such as linear chirp,qUadric chirp,bumps etc., and medical signals,such as ECG,EEGand EGG,etc., with high quality. The authors present a new optimization neural network, which can be called as constrained smallest smallest l1-norm neural network (CS11NN), to implement the Basis Pursuit (BP) [1] [2] [3] for high resolution time-frequency analysis. As the new and generalized one of the communities of overcomplete signal representations, the BP is considered as a large-scale linear programming problem. In contrast with the Simplex-BP or Interior-BP in [2], the proposed CSl1NN-BP dose not Taking non-stationary artificial signals and Electrogastrograms (EGGs) to test, our simulations show that the CS11 NN 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 (WD), but also than recently rising other overcomplete representation methods, such as Method of Frames (MOF) [9], Best Orthogonal Basis (BOB) [10 ] and Matc hing Pursuit (MP) [4]. Combining the high resolution with the fast implementation, the CSl1NN-BP will be very promising for on-line time frequency analysis of various kinds of non-stationary signals, such as linear chirp, qUadric chirp, bumps etc., and medical signals, such as ECG, EEG and EGG, etc., with high quality.