digital-communicationsModulation
So there are several ways to transmit a bitstream but where is the actual info when my carrier is a sinewave?
My basic understanding is we have symbols (phase,amplitude or frequency), we assign bits to these symbols and by modulating or changing those parameters (APSK,BPSK,FSK..) the receiver knows (or tries to decide) what got sent from the transmitter.
So the symbols can be seen as graphical representations of the associated bits?
The instantaneous frequency of a signal \$A\cos(\phi(t))\$ where \$\phi(t)\$ is an arbitrary function of time is defined as the derivative of \$\phi(t)\$ if you want to measure frequency in radians per second and as \$\frac{1}{2\pi}\$ times the derivaive_ of \$\phi(t)\$ if you want to measure frequency in Hertz. Of course, in the common case of a fixed frequency this corresponds to the familiar \$\phi(t) = \omega_c t+\phi_0 = 2\pi f_c t + \phi_0\$.
The standard definition of a frequency-modulated signal is one in which the deviation of the instantaneous frequency (at time \$t_0\$, say), from the carrier frequency is proportional to the value \$x_m(t_0)\$ of the modulating signal \$x(t)\$ at time \$t_0\$. The constant of proportionality is denoted by \$f_{\Delta}\$ in your notation: a \$1\$ volt signal creates a deviation of \$f_{\Delta}\$ Hz. Thus, if \$A\cos(\phi(t))\$ is the FM signal, then we have that $$ \left.\frac{\mathrm d}{\mathrm dt}\phi(t)\right|_{t=t_0} = 2\pi f_c + 2\pi f_{\Delta} x_m(t_0) $$ so that the deviation of the instantaneous frequency \$f_c + f_{\Delta} x_m(t_0)\$ from the carrier frequency \$f_c\$ is \$f_{\Delta} x_m(t_0)\$, just as we want it to be. It then follows from the fundamental theorem of calculus that $$\phi(t_0) = \int_{0}^{t_0}2\pi f_c + 2\pi f_{\Delta} x_m(t_0)\, \mathrm dt = 2\pi f_c t_0 + \int_{0}^{t_0} 2\pi f_{\Delta} x_m(t_0)\, \mathrm dt$$ or, with a slight change in notation, the FM signal can be expressed as $$A\cos\left(2\pi f_c t + \int_{0}^{t} 2\pi f_{\Delta} x_m(\tau)\, \mathrm d\tau\right)$$ the way you have it. Note that \$A\$ is the amplitude of the FM signal and is fixed; it is the frequency that is varying. Surely we need to distinguish between the FM signal when it is created using a voltage-controlled oscillator with an amplitude of \$1\$ volt and when it comes out of the power amplifier and goes to the antenna with a power of 10 kW?
The best way to go about doing this is basically bypassing the DDS altogether and generating the baseband from a DSP and generating the symbols using a IQ Modulator. A VCO based PLL can be used to generate an LO for the modulator.
Additionally, the magnitude of the I & Q baseband voltages has the following relation:
Vq = -tan(10°) * Vi
Vq = -tan(-10°) * Vi
Best Answer
Your unmodulated carrier is a sine wave. When modulated it can look like this: -
That's called On-Off-keying (OOK) and very similar to morse code. It could look like a version of OOK called ASK (amplitude shift keying): -
And below is an image of ASK, FSK and PSK: -
The words you use do not ring true. Look at the pictures.