# [chuck-users] phase modulation and hard sync?

mario buoninfante mario.buoninfante at gmail.com
Sun Jun 4 03:24:40 EDT 2017

```Hi Alexandre,

about FM and PM (probably my reply is late!), here's a simple
implementation using oscillators with sync(0):

/// m = mod osc;  c = carrier osc;//
//SinOsc m => Gain g => SinOsc c => dac;//
//Step cm => g; //cm = carrier freq in Hz//
//
//
//while( true ){//
//    modInd(10, 250); //arg: modInd, freq mod //
//    cm.next(500);////carrier frequency
//    second => now;//
//}//
//
//fun void modInd( float i, float f ){ //arg: modInd, freq mod//
//    float am; //
//
//    i*f => am; //(modInd = Am/Fm), then (Am = modInd*Fm)//
//    m.freq(f);//
//    m.gain(am);//
//}/

this is the simplest modulation, that usually is considered as FM, but
in the end is a PM.

without going into details, what's happening is:

FM (t)=sin(ω c t +Φ c + I sin (ω m t +Φ m ))

with ω c = carrier freq, ω m = mod freq, Φ = phase

Cheers,
Mario

On 04/06/17 07:34, Alexandre Torres Porres wrote:
>
>
> 2017-06-04 2:35 GMT-03:00 Alexandre Torres Porres <porres at gmail.com
> <mailto:porres at gmail.com>>:
>
>
>     It's not easy to explain, but you found the magic number/formula
>     that makes Frequency modulation sound like Phase Modulation.
>
>
> Actually, I shouldn't have said this, I don't wanna give you the idea
> it comes down to this, but there are just too many details I didn't
> want get into, sorry. What I can say is that you got pretty close, not
> 100% there yet, and that is not as simple as just doing this every
> time, it gets more complicated.
>
> Sorry again for not getting into the math and everything. What I'd
> like to add is that people use phase modulation instead of trying to
> replicate it via frequency modulation cause it's just more convenient
> to do directly via phase modulation if you want it to behave like that.
>
> cheers
>
>
>
>
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