In your example, what are the "pitch parts" you're separating when analyzing the two
oboes SINE waves - right Not square or some other arbitrary function.

Since I can only read the fragmented summary in the referenced paper, so maybe I'm
understanding it totally incorrectly. But it may not be relevant since the harmonic phase
relations don't appear to be held constant. In other words yes, you can get a sine if you
add two signals of different shape. Which is not what the poster asked.

I believe the poster was wondering if any function can be transformed from a non-circular
plane - like a square or rectangular one. Maybe it's just my limited knowledge, but I
haven't heard of such a thing. I can try to *approximate" a sine from a square plane...

--- In Doepfer_a100@yahoogroups.com , "Doug" <dougc356@...> wrote:
>
> Pretty sure my original post on this subject is weak (or worse), but
> I think this article might help. One should be able to construct an
> arbitrary periodic function using a non-trigonmetric basis. In other
> words, you *can* "create a sine by adding signals."
>
> http://ieeexplore.ieee.org/iel5/31/23557/01085543.pdf
> arnumber=1085543
>
> Further, seems to me the ear can be trained to listen for non-sine
> basis functions (aka "overtones"). Take for example, the sound of
> two or more oboes. Pretty sure one could separate the parts by
> pitch, although the parts aren't themselves pure sines. Muting one
> of the oboe parts would be filtering that "frequency", wouldn't it
>
> I guess I am agreeing with the original poster, and the answer as to
> why we analyse signals in terms of trigonometric basis functions is
> just mathematical (and design ) convenience.
>
> Doug
>
>
> --- In Doepfer_a100@yahoogroups.com , "laryn91" <caymus91@> wrote:
> >
> > I don't believe you can create a sine by adding signals with
> overtones. You can transfer the
> > energy around in the spectrum with specific phase cancellations.
> But every time you
> > cancel an overtone you create or reinforce another.
> >
> > In nature, sine functions are prevalent everywhere. On the other
> hand, square waves are
> > non-existent and must always be synthesized. It would very
> atypical for nature to miss
> > something as mathematically elegant as sines in favor of something
> more convoluted.
> >
> >
> > --- In Doepfer_a100@yahoogroups.com , "Monroe Eskew"
> <monroe.eskew@> wrote:
> > >
> > > I'm curious about harmonics. I've been looking for an
> explanation of why
> > > different waveforms have different overtones. One explanation
> offered is in
> > > terms of Fourier series. Every periodic function can be
> expressed as an
> > > infinite sum of sine waves of increasing frequency and
> decreasing amplitude.
> > > If we look at the Fourier series for a given curve (like a
> sawtooth or
> > > square wave), then we can find the overtones by looking at the
> terms in the
> > > sum.
> > >
> > > Now I like mathematics, but I'm not satisfied by this
> explanation. We can
> > > express a function as a Fourier series, but we can also express
> it in other
> > > ways. Perhaps a sine wave can be expressed as an infinite
> series of square
> > > waves. Then a sine wave should have a lot of overtones.
> > >
> > > Here's my guess-- Qualitatively, different waveforms have
> different sounds,
> > > and this does not necessarily need to be interpreted as having
> overtones.
> > > However FILTERS are what truly reveal overtones. But the
> function of a
> > > filter is determined by the fact that its resonant frequency is
> always a
> > > sine wave. If we had square wave resonance, then we'd have
> totally
> > > different filters, with the square wave being the least affected
> by the
> > > filter.
> > >
> > > Is that more or less correct
> > >
> > > Also, does the Fourier expression make the most sense to the
> human ear
> > > (i.e. Does the human ear have something akin to sine wave
> resonance )
> > >
> > > Thanks,
> > > Monroe
> > >
> > >
> > > [Non-text portions of this message have been removed]
> > >
> >
>