# SOQPSK-TG pulse shaping

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.

I can just accept for now that there is a time shift by L*T/2, so I can adjust my integration indices, and shift everything in time, no big deal: 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?