rickman wrote in :

On 10/7/2014 2:07 PM, gareth wrote:
"Ralph Mowery" wrote in message
...
I thought the triangle wave had even harmonics in it, but found out it
actually has odd harmonics but they decrease with the square of the order
instead of just a simple 1/N.

It is the sawtooth (equal slopes at rise and decay) that is made up of
even harmonics.

You seem to have them backwards...

http://en.wikipedia.org/wiki/Triangle_wave

http://en.wikipedia.org/wiki/Sawtooth_wave


(I cannot speak with any authority in the triangle wave)

Or much authority in the sawtooth wave as it turns out...


Well, he's not far wrong as it happens... I'm new to RF and radio but have
spent a lot more time with audio synthesisers. A triangle is a special case
of a sawtooth (properly, ramp) wave. Like the square, it has no even
harmonics, but the moment you change the speeds of the two parts of the ramp
in one cycle, even harmonics occur with increasing strength the more it gets
skewed. The really awkward bit with sawtooth waves is that they are a VERY
general case, and include ramps but also nonlinear slopes. This is something
I don't get into with maths, but it has strong implications for timbres
especially when emulating natural instruments like brass or strings or even
old synths that used relaxation oscillators. In radio techniques I imagine
the clipping and filtering (or other means) to precondition a rough signal
for the XOR phase comparator input of a PLL, taking advantage of its high
noise immunity even with the raw clipped signal (it still requires a 50%
width ratio), though a bit of filtering after clipping can help there.