Originally Posted by greeniguana00
People are incorrectly using this to say that a crossover will separate these harmonics.
It's not incorrect. A crossover WILL absolutely separate harmonics.
Look at it this way: if you have a 100 Hz sine wave and a 3100 Hz sine wave that are mixed, sent through an amp, and then into a passive crossover set to split at 800 Hz, it is clear that the wave at 100 Hz will go to the woofer, while the wave at 3100 Hz will go to the tweeter. This should be apparent - if it isn't, then there is a major understanding gap here.
It is also clear that 3100 Hz is one of the harmonics of 100 Hz, and would be present in a 100 Hz square wave.
Now, there is absolutely NO difference between the 3100 Hz signal by itself or acting as a component of the 100 Hz square wave. The crossover will push the energy in the 3100 Hz signal to the tweeter either way, with no difference in the net effect.
A sine wave also IS the sum of an infinite series of square waves (that I haven't quite figured out yet).
It's not an infinite series, per se, but you can can generate a sine wave with square waves followed by a reconstruction filter acting at the Nyquist frequency. This is a totally different principle, however, from the understanding of the harmonic content of a waveshape, and how a signal processor will act on it. [A passive crossover is a rudimentary signal processor, and the math is the same.]
I don't know what you mean by "intensity" but I hope you are using it in the right way.
I mean the energy present in the input signal in that frequency range. This is a basic integral function.
Pink noise is a great example. Pink noise is generated specifically to have equal energy in each octave - this makes system tuning much easier. Now, if you start at 20 Hz, it's fairly obvious that you have ten octaves' worth of information before you get to 20 kHz. Thus, if you have a 100W total power pink-noise signal, there will be 10W of power in each octave. Here's the kicker: Since the energy is equal-per-octave, the bands from 20-2,560 Hz will contain 70 W of that energy, while the remaining 30 W will be spread from 2560-20kHz.