Add, subtract, multiply, divide, logic operations ...

[Analogue Information]

> >I still don't understand.  If you add the instantaneous voltages of
> >two signals, you're mixing them, right?  or what distinction am I
> >missing?
> 
> No. This can't be true, and it *JUST* dawned on me as to why...

I'm afraid it is.

> But... If I ADD them together I will *THEN* get a single pitched tone, but
> it will have twice the voltage at the peaks and the SLOPE of the viewed
> waveform will be twice as steep. It will be much more triangle than sine.
> 
> Lemme do the numbers again (and I'll do 'em right this time <g>):
> 
> 	sine #1   -3 -2 -1 0 +1 +2 +3 +2 +1 0 -1 -2 -3 -2
> 	sine #2   -3 -2 -1 0 +1 +2 +3 +2 +1 0 -1 -2 -3 -2
> 	sum	   -6 -4 -2 0 +2 +4 +6 +4 +2 0 -2 -4 -6 -4

Umm, if you feed a signal into your stereo, a sine wave, for instance, then
attach a scope to the speaker terminals, watch as you turn up the volume,
what do you get ?    You get a sine wave where the zero crossover points
never change but the amplitude does, since the peaks get taller, yes the
slope changes, you have defined amplification quite nicely.

> 
> The frequency of this waveform will be the same (the zero crossings will
> occur at the same place in time), but the peaks are twice the value, hence
> twice the "volume", and since the voltages are changing faster and covering
> more "distance" to reach the same point in time, then the slope must be
> greater. No more sine wave.
> 

Umm, louder sine wave, now matter how steep the slope of the walls becomes
it still gradually declines to zero at the peak of the wave, is still a sine
wave.

> If you accept this for an example of two sines at the same frequency, then
> the same must be true for two sines of different frequencies, and any
> number of complex waveforms at any number of frequencies.
> 
> Here's my other example, but sdone correctly:
> 
> 	wave #1   -3 -3 -2 -2 -1 -1  0  0 +1 +1 +2 +2 +3 +3
> 	wave #2   -3 -2 -1  0 +1 +2 +3 +2 +1  0 -1 -2 -3 -2
> 	sum	   -6 -5 -3 -2  0 +1 +3 +2 +2 +1 +1  0  0 +1
> 
> >From the looks of this.... It's gonna be awhile befor the final waveform
> ever gets back below the zero crossing. This could be quite cool...

let's see adding sine waves of different frequencies, that would be additive
synthesis right.  This does indeed result in different timbres, perhaps
someone with a good understanding of harmonics can alaborate, however, no
secret here you can achieve the same effect by feeding sine waves of
different frequencies into your mackie.

> 
> 
> If you then go back to what Bert originally was looking at... I think that
> we'd *ALL* want a module like this...
> 

You're still not quite understanding this.  It's just mixing.  Let's take an
example from a previous post. If you apply a one volt signal to fourty
inputs of a mixer with each channel set at unity gain then you will indeed
have a 40 volt signal on the buss.  Of course this doesn't happen, why, two
words "attenuation", "distortion"  Your mixer is limited by it's own
technology which probably includes opamps so I will use that as an example
although it doesn't really matter if it does or doesn't (just trying to
avoid another tangent) Opamps usually have a +-15 volt supply so you are
limited to something less than that on the outputs, what happens when you
try to force it to fourty volts, distortion, clipping, that's what.  Which
is why mixers are a combination of summing amplifiers and attenuators.
Mixers sum and attenuate at the same time giving you a combination of the
input waveforms at a similar level.


> Think about *really* dividing waveforms... wow.
> 
> This sounds like it'd be right up Serge's alley... Anyone wanna run this by
> Rex and see what he has to say?

As was explained earlier, multiplying, think ring modulation.

Daryl