The sampling rate for our transmitter is defined by the channel - 8000 per second. This is not a multiple of the baud rate (i.e. 2400 baud). The baud interval is actually 10/3 sample periods. Generating at the lowest common multiple of the baud rate and channel sample rate (i.e. 24000 samples/second), and then decimating to 8000 samples/second, would give good results. However, this would require considerable computation. A shortcut is to use slightly shaped pulses, instead of simple square ones. We can achieve the effect of pulse transitions at the 1/2 and 2/3 sample points by adjusting the first sample of each new pulse. The adjustment is simple. We need the effect of being 60 degrees or 120 degrees through a sine wave cycle at the Shannon rate at the sample point. This simply means we need to step by 0.25 or 0.75 of the actual step size on the first sample of those pulses which should start at the 1/3 or 2/3 sample positions. The logic and computation needed for this is much less than the computation needed for oversampling at 24000 samples/second.
The pulse shaping filter is only vaguely defined by the V.29 spec. Some of the other ITU modem specs. fully define the filter, typically specifying a root raised cosine filter, with 50% excess bandwidth. This is a pity, since it increases the variability of the received signal. However, the receiver's adaptive equalizer will largely compensate for these differences. The current design uses a root raised cosine filter with 50% excess bandwidth.
The carrier is generated using the DDS method. Using two second order resonators, started in quadrature, might be more efficient, as it would have less impact on the processor cache than a table lookup approach. However, the DDS approach suits the receiver better, so the same signal generator is also used for the transmitter.