In article <hinfjn$8s...@speranza.aioe.org>, Mel <mwil...@the-wire.com> wrote: >Alf P. Steinbach wrote: >> * Steve Holden: > >>> It's not clear to me that you can approximate any waveform with a >>> suitable combination of square waves, >> >> Oh. It's simple to prove. At least conceptually! :-) >> >> Consider first that you need an infinite number of sine waves to create a >> perfect square wave. >> >> The opposite also holds: infinite number of square waves to create a >> perfect sine wave (in a way sines and squares are opposites, the most >> incompatible). > >No, it doesn't. The infinite set of sine waves that make a square wave >leave out the sine waves of frequency 2f, 4f, 6f, 8f, ... (2*n*f) ... . >Once you've left them out, you can never get them back. So sawtooth waves, >for example, can't generally be built out of sets of square waves.
Bullshit. My Boehm (B\"ohm) electronic organ does exactly that. They even have a chip for it. In the 70's it was a great hype, a sawtooth organ. Well not exactly a hype, the sound, especially the low registers, is dramatically better. If you're interested in frequencies above audible (organ builders aren't), you need an infinity of squares to build a perfect sawtooth. But then you need an inifinity of sines to build a perfect square wave. <SNIP> > Mel. Groetjes Albert -- -- Albert van der Horst, UTRECHT,THE NETHERLANDS Economic growth -- being exponential -- ultimately falters. alb...@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst -- http://mail.python.org/mailman/listinfo/python-list