Very often we apply to circuits sinusoidal or constant voltages, and we study methods (like the phasors method) to analyze them. Here's a simple question to which, in many years, I have found not yet an answer: how can it be possible that a signal starts from -infinity and goes to +infinity? When studying sinusoidal circuits, every text applies a sinus or cosinus input (which never has a beginning), but there must be an exact moment in which the circuit switches on.
Another question: if I consider amplitude modulation, we know that a generic signal m(t) must be multiplied by cosinus in order to shift its spectrum, then the receiver will build again the original signal in some way, which is now not important. The questions are:
1st: the cosinus which multiplies m(t) in theory starts from minus infinity and finishes in + infinity; in reality every phisical signal must have a beginning, then: how theory would be modified if I consider a "real" signal (=a signal which has a beginning and a stop)?
2nd: In the theory of AM, the signal m(t) is already known (I mean, I can plot the graph of the function, I know m(t) in every instant), then I know for sure its spectrum. But if I think to a radio presenter, when he speaks the signal does not yet exist, I mean: m(t) is a "real time" signal, I don't know m(t) in every instant but it is "under construction". As a consequence, I don't know its spectrum and it seems to me that all the theory of AM is no more valid.