seanadams wrote: > Pat Farrell;231200 Wrote: >> Right. That's real likely. > Pat, I don't really get what you're saying here. Is it that you believe > the Shannon Nyquist theorem is incorrect, or do you believe that a > band-limited square wave can not be expressed as a finite sum of sine > waves, all below said band limit? This is pretty fundamental stuff... > the latter statement is true simply by _definition_ of "band limited".
I believe in Shannon. I think we are talking past each other, probably in violent agreement. I don't believe that real square waves happen. They never happen in music, and even with a signal generator, the LRC network of any wiring will round off the sharp edges to some degree. You use a signal generator capable of 100kHz or more to make even a vaguely square 20kHz square wave. The resulting almost square wave is more clearly a sum of high frequency sine waves. With rounded edges, you don't need to go to infinite frequencies and infinite sums. > Pat Farrell;231200 Wrote: >> Round the numbers to make it easier to see. >> 20kHz square wave, sample at 40kHz. >> result is 1, -1, 1, -1, 1, -1, ... >> > > You've chosen an especially poor example here because in this case > 20KHz is at exactly the Nyquist frequency. Yes, its poor, I picked it and the phase points being sampled on purpose. Not much changes if you sample that same square wave at twice the rates, which I also showed. > But that aside, the important point here is that you've forgotten the > step where said 20KHz square wave is filtered before sampling. When you > remove content above 20KHz, what you end up with is a perfect 20KHz sine > wave. Not me, its others that are talking about 20kHz square waves being important. There has been a lot of pseudo math in this thread. That's why I posted up thread that the keys are the mathematics of Taylor series and Maclaurin series, which predate Shannon's theory. > This is the basis of what opaqueice stated earlier. The ONLY difference > between a 20KHz square and a 20KHz sine is at 60KHz and up. Band limit > them and they're identical. That may be true, but I sure didn't read it that way. Even at 60kHz sampling, your square wave ain't gonna be square when you recreate it. If you look at music, there is damn little signal above 10kHz. A few overtones, most of them way down in level relative to the fundamentals in the 200 to 3,000Hz range. _______________________________________________ audiophiles mailing list [email protected] http://lists.slimdevices.com/lists/listinfo/audiophiles
