🚀 go-pugleaf

In article <1992Dec30.064222.9259@netcom.com> gerg@netcom.com (Greg Andrews) writes:
\walvdrk_r@research.ptt.nl (Kees van der Wal) writes:
/\I believe the book. The book say that symmetric waveforms have no even
\/harmonics, so the probably symmetric 25 or 33MHz clock has to be converted into
/\something asymmetric to be useful.
\/
/
\What does your book say about a Sawtooth (Ramp) wave?
/
\
/      /|    /|    /|    /|    /
\     / |   / |   / |   / |   /
/    /  |  /  |  /  |  /  |  /
\   /   | /   | /   | /   | /
/  /    |/    |/    |/    |/
\
/According to my reference, a Sawtooth wave has both odd and even harmonics,
\whose amplitude is inversely proportional to the harmonic number itself.

Quite so.  But a sawtooth wave is hardly symmetric.  Turn the picture
upside-down and you'll see--the ramp part now runs the other way.

A triangle wave, on the other hand, is symmetric:

	/\    /\    /\    /\
       /  \  /  \  /  \  /
	   \/    \/    \/

And, it has no even harmonics.  The absence of even harmonics in symmetrical
waveforms can be proven with fourier analysis.  (I'll save you the details,
but they aren't hard to look up.)

		-Ed Hall
		edhall@rand.org