Abstract
This paper introduces in detail the optimal design approach of high-order digital differentiator based on the algorithm of neural networks. The main idea is to minimize the sum of the square errors between the amplitude response of the ideal differentiator and that of the designed by training the weight vector of neural networks, then obtaining the impulse response of digital differentiator. The convergence theorem of the neural-network algorithm is presented and proved, and the optimal design approach is introduced by examples of high-order digital differentiator. The results show that the high-order digital differentiator designed by training the weights of neural networks has very high precision and very fast convergence speed, and initial weights are stochastic. Therefore, the presented optimum design method of high-order digital differentiator is significantly effective.
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