I don't fully understand your situation but ann, especially MLP, works generally in various regression, curve fitting. In supervised learning you just need to train your MLP with the target values which you want to fit. Despite little error between target values and the output of MLP, it will show good results.

What I exactly need is considering a neural network black box, to which I give my input which is an Ampliude Modulated wave and the output must be the envelope of the input signal. 

In that situation, your target values must be the envelope of the input signal. You need to get the envelope of the input signal in advance by envelop detector, Hilbert transform or whatever.

Then you need to formulate feature vector for ANN with your input signal. What matters is how to build the feature vector.  

If you succeed in getting proper target values and feature vector, you just need to train your ANN. Of course you should be able to select proper model of ANN.  

I'd like to ask you refer to my paper " Pattern recognition-based real-time end point detection specialized for accelerometer signal" at    https://www.researchgate.net/publication/224586403_Pattern_recognition-based_real-time_end_point_detection_specialized_for_accelerometer_signal

In my case, I needed to estimate motion period with acceleration data. For target values, I had to mark motion period by pressing a button. 

Conference Paper Pattern Recognition-based Real-time End Point Detection Spec...

Once you compete training ANN, you just need to generate feature vector to ANN with new input signal. Then your trained ANN will give you its estimated output.

That was a nice explanation... can I do the same with any unsupervised learning techniques...  

Probably you can try it in unsupervised way but the results will not meet your expectation.