I actually did my undergraduate signals and systems course with McClellan (him as the prof too). His text is definitely one the best ones. Another one that I like a lot because of its completeness and the wealth of examples is this one.
Good luck!
You’re thinking of practical implementation issues where I said again and again I’m talking about theory (which is the thing you asked in your first reply). Any signal can be transformed into a frequency representation, which is unique and invertible. A finite, non-periodic signal has an infinite frequency domain representation (and vice-versa). The signal will not repeat, no need for window or envelope. For a practical synthesizer this is nonsense but we were discussing Theory, weren’t we?
RTFM:
https://www.amazon.com/Linear-Systems-Signals-2nd-Lathi/dp/0195158334