I asked this question already on the physics site but it was advised to ask it here. If a piece of music is played for an infinite amount of time (with a volume that you can hear) can it be decomposed in sine-, cosine, and the one-function? If the sound of music has a sine form it can surely be decomposed in a sine- form! But what about other non-periodical infinitely played music?
I know that if a piece of music is played for a finite time (say 10 seconds) it can be decomposed, just as an infinitely long played periodic sound can. but what about infinitely long aperiodic sound?
I know that there are conditions on the functional form to be Fourier transformed. The signal can be periodic and inifinite. The signal can have an infinite support bu the functional value has to reach for zero or be zero on both sides of the max of a signal. Can we apply the transform to a piece of endless music?