Re: Audio frequency and directionality question?

"RST Engineering (jw)" <jim@xxxxxxxxxxxxxxxxxx> wrote in message
news:11ort7aide2vv25@xxxxxxxxxxxxxxxxxxxxx
> Hm. Never needed to use the information, but as I recall my Fourier prof
> from college (admittedly 45 years ago) the square wave has all the odd
> harmonics and the triangle has all the even harmonics. Am I really
> disremembering that or did my prof screw up?

I don't remember these things well enough to trust myself, but I do trust
Wikipedia in this regard. "Like a square wave, the triangle wave contains
only odd harmonics. However, the higher harmonics roll off much faster than
in a square wave (proportional to the inverse square of the harmonic number
as opposed to just the inverse), and so its sound is smoother than a square
wave and is nearer to that of a sine wave." "A sawtooth wave's sound is
harsh and clear and its spectrum contains both even and odd harmonics of the
fundamental frequency."

What about the fundamental and all the even harmonics? Ignore the
fundamental for a moment; now what you have is 2f, 4f, 6f, ... so that's
the same as 1*(2f), 2*(2f), 3*(2f), ...; in other words, it's a sawtooth at
twice the frequency. Add the fundamental sine wave back in, and you get
something that looks sort of like a capacitor charging and discharging.
Hmm.


.

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