A novel periodic activation function was presented to replace the monotonously increasing type activation function commonly used in feedforward neural networks.To speed up the learning,as well as to reduce the network size,the extended Kalman filter(EKF) algorithm with a pruning method was suggested to train the network.This approach was applied to solve three typical problems,namely,4-point XOR logic function,sunspot series prediction and rotation-invariant classification.Simulation results show that,with the proposed periodic function,a two-layer perceptron (without the hidden layer) is able to solve the XOR problem.Moreover,the EKF algorithm and the pruning scheme also lead to a fast convergence nad a compact network for sunspot series prediction and rotation-invariant classification.