Here I demonstrate how much modulator modulates the carrier in the Heisenberg's phase modulation. The purpose is so that you know how much you're modulating based on modulation values. When the modulator's value is 0 (the value is in the range [-1,1]), no phase shift of the carrier occurs. The amount of phase shift is a positive linear function of the value of the modulator when the amount of modulation is constant. I set out to find the phase shift as a function of amount of modulation and value of modulator. I used the sawtooth down as the modulator because it is linear and starts at 1 and ends at -1, and a sine wave at 0 Hz as the carrier so that the phase is always (0 + phase shift). Note that there is an imperfection at the jump of the sawtooth wave because it's band limited. At modulation amount = 0, nothing is heard (no phase shift). At modulation amount = 50, a sine wave is heard at the modulator's frequency. This means that for every wave of the modulator, a wave of carrier is played. The carrier is shifted 1/2 wave at modulator = 1 and -1/2 wave at modulator = -1, or range [-π,π]. When the amount of modulation is 100, a sine wave is heard at 4 times the modulator's frequency (carrier shift is 2 waves at modulator = 1, -2 waves at modulator = -1, or range [-4π,4π]). I extrapolated from these two points that at a modulation amount of sqrt(3)*100/2≈86.603, the carrier would be shifted 3/2 wave in each direction (range [-3π,3π]), and at sqrt(2)*100/2≈70.711, it would be shifted 1 wave in each direction (range [-2π,2π]. I was correct so I could be reasonably certain that the phase shift is s = modulator*π*(2x/100)^2 where "s" is the phase shift in radians, "x" is the amount of modulation, and "modulator" is value of the modulator in [-1,1]. Alternatively, λ = (modulator*(2x/100)^2)/2 where λ is the number of wavelengths of the carrier. If you modulate the carrier using two modulators, then the phase shifts add.
Interestingly, when I was making my Weaver SSB freq-shift, I needed to make a coupled sinusoidal (sine & cosine pair) and so I needed to figure out the same thing. My method was different. I set had two oscillators Up Saw (OP A) and Down Saw (OP B), then a third oscillator a square wave with 0Hz, and I modulated oscillator B with this last oscillator.
Okay. I think you are right here. I had the sense that I was off.
No, that means that the phase is shifted by pi at 50%. Saw up + saw down = square happens when one of them is shifted 180 degrees.
If you sweep the modulation index from 0% to 100%, you see that you get silence thrice, where the first silence is 0%, second around 70.7% and the third at 100%. If you render it and inspect it, you'd also notice that you get a perfect square wave at 50%. This means that at 50%, the phase is shifted by 90 degree (pi/2). This matches with your findings as well, but the reason why your range [-pi, pi] for 50% is because you used a sawtooth, while my square wave would simply be a constant shift.
oh
you kinda had me in the first few sections but after you brought in pi you lost me idek wtf extrapolated means
helo
Xifed2.0
hey, open the remix
nerd.
Thanks. This helped.
well. im back at this again
rly good bass tho
nerds unite we out here
soooooooo complitated
If you're interested, here's some phase modulation, Heisenberg style. http://wavepot.com/anonymous/d74b38a26b885caf059e Clean example of what I demonstrated here (sawtooth wave is perfect). http://wavepot.com/anonymous/47d982462b27f950328c
and please send me back cuz im an eekweihshawn dumbass
Inavon, I am honestly confused. http://wavepot.com/potasmic/b4756718f4847fb9325c You can edit the code as you like and save it as a gist (no account requires)
The equations you wrote above is really weird. I'm testing in a DSP sandbox and it seems that either one of the equation is correct at certain value of the `amount of modulation`
Xifed.