jj@alice.UUCP (01/24/85)
Joel. About your point number 1), regarding music not being sine waves: ELEMENTARY communications theory shows you how to calculate the bandwidth of a varying amplitude sine wave. Given that, there is NO theoretical problem, small or large, with the fact that music does not consist of sine waves. Simply put, once you have calculated the bandwidth of the signal (hell, if you really want to get down to specifics, you can take the TRANSFORM of the WHOLE SONG and use that. It's a time-limited signal that will have an EXACT spectrum) you know that you can capture anything up to a given frequency in your digital representation. That's all there is to it. About your point 2). It's rather riddled with incorrect assumptions, your example is of a signal at exactly half the sampling rate that has INFORMATION WELL ABOVE half the sampling rate, and as such is just totally invalid. Simply put, a signal that is exactly at half the sampling rate cannot EVER change, or it has too much bandwidth, since it then splashes past the halfway point. A signal one Hz below half the sampling rate (I'm assuming the "perfect" filter, but the argument holds for different frequencies with imperfect filters) can be modulated by anything that has a bandwidth of less than one Hz and go through just fine. More than one Hz and you loose information. In other words, a rapidly varying tone near Fs/2 has signal components ABOVE Fs/2, and will HAVE to be filtered. Wozencraft and Jacobs book is perhaps too advanced to recommend, I suggest that you get a copy of Steiglitz's "An Introduction to Discrete Systems" and give it a good read. -- TEDDY BEARS PROTECT PENGUINS FROM WALRUSES "I wish I was home again, back home in my heart again, it's been such a time since my heart's home to me. ..." (allegra,harpo,ulysses)!alice!jj