JTDX and WSJT-X prebuild the FT8 message audio samples (at 48KHz) and send them altogether to the PC audio card whose output modulates the SSB (USB) transmitter. In this case, the task to precisely send out the 81 FT8 symbols is in charge of the audio card.

Of course I cannot follow this method because, as I explained in the log FT8 QSO's, I chose to use an external sinusoidal DDS synthesizer that I need to modulate in amplitude (for the 1st an 81st symbols only) and frequency for the whole 81 symbols. Therefore I need to change amplitude (8 bits encoded) and frequency (32 bits encoded) at a proper speed.

For the amplitude

The first symbol has a 20 milliseconds ramp-up (shaped as a raised cosine) and a remaining 140 milliseconds at constant amplitude

The last (81st symbol) has a 140 milliseconds duration at constant ampltude and a remaining 20 milliseconds ramp-down (shaped as a raised cosine)  

I suppose that I can approximate the raised cosine ramp-up o ramp-down with 20 samples (1 sample every millisecond). E.g. 0 0.01 0.02 0.03 0.05 0.07 0.10 0.15 0.20 0.40 0.60 0.80 0.85 0.90 0.93 0.95 0.97 0.98 0.99 1

For the Gaussian Frequency Shift Keying

The frequency change is every 160 milliseconds (1 symbol duration) but it is smoothed with a Gaussian function, to reduce band occupation. MYJTDX produces the frequency shift samples at 48KHz so that, for every 160 milliseconds symbol we have 7680 samples. The maximum shift (from value 0 to value 7) is 7 * 6,25 Hz=43,75 Hz and can happen in about 32 milliseconds (0.2 * 160 milliseconds)