Doepfer

How can you have negative frequencies?  Frequency is cycles per second...
How do you get a negative number of cyles??


[Non-text portions of this message have been removed]

On Thu, May 22, 2008 at 11:16 AM, Monroe Eskew <monroe.eskew@gmail.com> wrote:
> How can you have negative frequencies? Frequency is cycles per second...
> How do you get a negative number of cyles??

IIRC, it's not exactly negative frequency, it's just a flipped phase.
IE, at 1hz it's one cycle per second with standard phase, as you
approach 0hz the waveform stops varying, and as you approach "-1hz"
the waveform travels in the opposite direction, such that at "-1hz"
it's the same frequency as at 1hz but with inverted phase
relationship.

-Brandon

But what exactly is "traveling in the opposite direction?"  If you graph out
voltage vs. time, then there is only one direction to go since, absent a
flux capacitor, time marches on in a "forward" direction.
Do they just mean that the voltage is inverted when you set the thing below
zero?  One can easily achieve that with other modules...

-Monroe

On Thu, May 22, 2008 at 12:28 PM, Brandon Daniel <bdu@fdiskc.com> wrote:

>   On Thu, May 22, 2008 at 11:16 AM, Monroe Eskew <monroe.eskew@gmail.com<monroe.eskew%40gmail.com>>
> wrote:
> > How can you have negative frequencies? Frequency is cycles per second...
> > How do you get a negative number of cyles??
>
> IIRC, it's not exactly negative frequency, it's just a flipped phase.
> IE, at 1hz it's one cycle per second with standard phase, as you
> approach 0hz the waveform stops varying, and as you approach "-1hz"
> the waveform travels in the opposite direction, such that at "-1hz"
> it's the same frequency as at 1hz but with inverted phase
> relationship.
>
> -Brandon
>
>  
>


[Non-text portions of this message have been removed]

On Thu, May 22, 2008 at 12:35 PM, Monroe Eskew <monroe.eskew@gmail.com> wrote:
> But what exactly is "traveling in the opposite direction?" If you graph out
> voltage vs. time, then there is only one direction to go since, absent a
> flux capacitor, time marches on in a "forward" direction.
> Do they just mean that the voltage is inverted when you set the thing below
> zero? One can easily achieve that with other modules...

Imagine this scenario:

Basically, apply 1v to the pitch input, output is a rising sawtooth.
Ramp the input down to 0v, it reaches 0v at the input right as the
sawtooth hits 0v travelling upward, so the output is also 0v.
Ramp input down to -1v, output begins to travel from 0v down towards
negative max v, and waveform is falling sawtooth.

-Brandon

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.
Thanks,
Monroe

On Thu, May 22, 2008 at 1:20 PM, Brandon Daniel <bdu@fdiskc.com> wrote:

>   On Thu, May 22, 2008 at 12:35 PM, Monroe Eskew <monroe.eskew@gmail.com<monroe.eskew%40gmail.com>>
> wrote:
> > But what exactly is "traveling in the opposite direction?" If you graph
> out
> > voltage vs. time, then there is only one direction to go since, absent a
> > flux capacitor, time marches on in a "forward" direction.
> > Do they just mean that the voltage is inverted when you set the thing
> below
> > zero? One can easily achieve that with other modules...
>
> Imagine this scenario:
>
> Basically, apply 1v to the pitch input, output is a rising sawtooth.
> Ramp the input down to 0v, it reaches 0v at the input right as the
> sawtooth hits 0v travelling upward, so the output is also 0v.
> Ramp input down to -1v, output begins to travel from 0v down towards
> negative max v, and waveform is falling sawtooth.
>
> -Brandon
>
>  
>


[Non-text portions of this message have been removed]

--- In Doepfer_a100@yahoogroups.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/

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]
>

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@namshub.ch>
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]

--- In Doepfer_a100@yahoogroups.com, "omegaattraktor" 
<omegaattraktor@...> wrote:
>
> --- In Doepfer_a100@yahoogroups.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/


exactly. a standard vco will stop oscillating at 0 hz,
it even cannot reach 0 hz at all because of technical issues
within the vco design. a standard vco can never have more
than 100% linear fm.

a thru-zero vco can handle more than 1000% linear fm, because
it can go "through" that 0 hz barrier into "negative" frequencies, 
which means that the waveform reverses direction, not it's phase.
it's a bit like driving a car in reverse gear.

example, a vco sinewave cycles between +5 and -5. lets say that at
one given point the waveform has an amplitude of +1 volts
and is on its way down, towards -5 volts. when the thru-zero vco
reverses direction at that given point then the waveform will
continue at +1 volts amplitude, but going up towards +5 volts.
while the facts are quite boring, the sonic differences are huge.

best wishes

ingo