Neural networks for signal transform

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I am wondering, if there is an example code doing signal transform using neural network?

I am formulating my question in following steps:

I have a input signal x and its output y. So the x goes through the whole network and eventually becomes y.

So conceptually, if I have a bunch of x and a bunch y, I should be able to converge those weights in the network, such that next time when I throw a new x into the network, a corresponding new y will generated based on the training the network had.

So simply, through training, I will have my own transformeor/operator that turns x into y.

Is there such an code package? Or am I looking for something not existing? The reason is because this problem sound very fitting the neural network nature.

Thanks a lot.

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