I'm trying to build an SOQPSK-TG signal in MATLAB/Octave. I am following this paper for formulas.
I'm trying to generate a waveform for the phase, equation 2.4:
Where q(t) is the phase pulse, equation 2.3:
f is the partial-response frequency pulse (L=8 for SOQPSK-TG):
and w is the window function:
for SOQPSK-TG, we have the following values:
p = 0.7, A = 0.3112, B = 1.25, T1 = 1.5, T2 = 0.5, L = 8, h = 0.5, T = 1
One point of confusion I am seeing is that when I plot ftg(t) as written, the pulse is centered around t=0:
However the image of ftg in the paper shows an unexplained shift in time:
The formula for q(t) also supports this time shift, showing that the integral must start at t=0, and should end up at 0.5.
When I plot the resulting phase using the time shifted version of ftg, I end up with a smooth moving waveform, which is the desired behavior:
However, when I look at the mod(2*pi) results, and sample once per symbol-duration-period, I am seeing 8 discrete phase states:
The document claims I should only see 4 discrete phase states. Interestingly enough, if I don't time shift ftg, I end up with a non-smooth phase state:
But with this waveform I am seeing the 4 discrete phase states:
How can I get a smooth looking waveform with 4 discrete phase states?