How to "draw" the function/wave to send symbols using QAM? Say you have the following 8QAM constellation diagram:



Say, you want to send the sequence:

001 110 101 000 001

How would you draw the function/wave containing the symbols?

My problem in understanding this is:

I know you use amplitude and phase shifting for defining symbols. Each symbol has a complex function like this:

$$g(t) = A \times e^{i(ft + \phi)}$$

($A$ = amplitude, $f$ = frequency, $\phi$ = phase)

You have one function for each of the possible symbols. But how do you draw the sequence of symbols (or even one symbol)? Isn't $e^{ix} = \mathrm{cos}(x) + i \times \mathrm{sin}(x)$ ? Do I draw the real part or the imaginary part?

Thanks!
The baseband QAM signal is complex, and the only way to draw it is by doing two drawings, one for the in-phase (real) component, and one for the quadrature (imaginary) component.

The passband QAM signal, though, is real, and it is a pulse-shaped carrier whose amplitude and phase depend on each symbol. Myself, I would "draw" it using Matlab or some other numerical program. I don't see the point in trying to draw it by hand.

For example, in Matlab, assuming QPSK and transmitting three symbols with a rectangular pulse shape, at a rate of one symbol per second and a carrier of 5 Hz:

t = 0:0.01:2.99;
p = ones(1,100);         % pulse shape
s = [1+1i, -1-1i, 1-1i]; % symbols to transmit
u(1:100:201) = s;
qam_bb = conv(u,p);      % pulse shaping to generate baseband signal
subplot(3,1,1);
plot(t,real(qam_bb)); title('Baseband In-Phase'); axis([0 3 -1.3 1.3]);
subplot(3,1,2);
plot(t,imag(qam_bb)); title('Baseband Quadrature'); axis([0 3 -1.3 1.3]);
qpsk = real(qam_bb.*exp(2*pi*5*t*1i));  % upconvert baseband signal
subplot(3,1,3);
plot(t,qpsk); title ('Passband QPSK');


produces this plot: