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OP I was teaching amplitude modulation in class today and the professor who is sitting in my class to teach it next semester came to me at the end and said "I bet this is where pushing the envelope comes from" I said, I will ask. Envelope is the message signal which is off set by a constant value to avoid synchronization at the receiver. If the off-set is too much, the message signal (the envelope) is pushed up too high and gets distorted. Since AM radio comes before WWII, maybe they borrowed the term.
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