I believe the confusion is calling it positive and negative "frequencies". The frequency
doesn't change - only the cycle direction.

Here's another way to visualize it: a sine wave can be drawn by moving a point around a
circle and plotting its Y axis displacement on a linear strip chart. Each revolution around
the circle makes one cycle so the velocity of rotation sets the frequency. The strip chart is
always moving forward representing positive time.

If you move the point around the circle in a CW direction you get positive frequencies.
Likewise CCW rotation produces "negative" cycles.

Like reversing the tone wheels in a Hammond organ.

--- In Doepfer_a100@yahoogroups.com , "Monroe Eskew" <monroe.eskew@...> wrote:
>
> To describe a sine wave mathematically we write the voltage function of time
> as
> V(t) = sin(ct)
>
> where c is a constant. We can show that c is in fact the frequency, or
> cycles per unit time (if we normalize to radians). c may be taken to be
> negative, but in all cases we have the identity:
>
> sin(-ct) = -sin(ct)
>
> Therefore "negative frequencies" can be achieved by setting the oscillator
> to the corresponding positive frequency of equal magnitude and running it
> through a voltage inverter. Now, turning the frequency dial through zero
> from c to -c is a much different transform than feeding a frequency +c
> signal through a polarizer and turning the polarizer from +1 to -1. But the
> start and end points are the same.
>
> -Monroe
>
> On Fri, May 23, 2008 at 2:27 AM, omegaattraktor <omegaattraktor@...>
> wrote:
>
> > --- In Doepfer_a100@yahoogroups.com <Doepfer_a100%40yahoogroups.com>,
> > "Monroe Eskew" <monroe.eskew@>
> > wrote:
> >
> > >
> > > That sounds like thru-zero amplitude modulation, which is nothing new,
> > > though it is a nice feature to put within one module. But thru-zero
> > > frequency modulation Still confused.
> >
> > negative frequencies has nothing to do with inverted phase. it means
> > that the signal is going its way back. but of course the time continuum
> > will not be affected. this can happen at any amplitude of the signal,
> > therefore it doesn't invert the phase.
> >
> > negative frequencies do occur with large amount of fm. imaginge the
> > frequency of an osc with 1kHz is modulated by another osc. if the
> > amount of modulation is increased there is a point when the frequency
> > is modulated between 0kHz and 2 khZ. if you increase the modulation
> > further the frequency finally goes to negative. thru-zero fm just means
> > that an osc can handle this.
> >
> > regards,
> > oliver
> >
> > http://www.namshub.ch/
> >
> >
> >
>
>
> [Non-text portions of this message have been removed]
>