Nonlinear filter design using artificial neural networks

The advantages and difficulties in training a neural network to emulate various types of filters are described. For the normalized low-pass filter, a multilayer perceptron is trained with various sets of sinusoids. The trained network shows superior performance for the training signals with almost negligible phase distortion. However, the network's performance for linear combinations of training signals is poor. Moreover, the network's performance deteriorates as the number of sinusoids superimposed on the input increases. This seems to be caused by the inherent nonlinearity of the network. The performance in general improves as the number of training sinusoids increases