With a digital signal, a sine wave can naturally only be predicted with a square wave.

As to my knowledge, no consistently profitable system has so far been realized with a neural net, despite lots of various attempts. This is of course even more true for perceptrons, hidden layer or not. So I would not have much hope of success with an improved perceptron. More interesting for trade systems are the pattern finder and the decision tree. The pattern finder is interesting because mildly profitable systems have been realized with it by some technical traders, f.i. the Asirikuy group. And decision trees have little been used so far for trading, so they are a new area and experiments with them could be interesting.