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For a lumped nonlinear modeling of the relationship between input and output sequences, Discrete Synapse Recurrent Neural Network (DSRNN) is proposed using fully Recurrent Neural Network (RNN) structure and Extended Kalman Filter (EKF) algorithm for its training. The training process is more efficient and there is less output error and more stability than in the previous study using feedforward networks. DSRNN is applied to a task of seismic signal classification to discriminate footsteps and vehicles from background. Temporal features of the signals were modeled using data recorded in the deserts of Joshua Tree, CA. The proposed classifier showed 0.3% false recognition rate for the recognition of human footsteps, 0.9% for vehicle, and 0.0% for background. The models were able to reject quadrupedal animal's footsteps (in this study a trained dog). The system rejected dog's footsteps with 0.2% false recognition rate.