F5OEO has recently written some code to transmit a SSB signal using just the hardware in the Broadcom SOC chip on the Raspberry Pi. You can find more info on this link http://www.rtl-sdr.com/transmitting-fm-am-ssb-sstv-and-fsq-with-just-a-raspberry-pi/
I tested the code on my RPI on 6m via a cable connection. It worked OK. If you look at the S-meter you can see that the envelope is constant. This is due to that the RPI has no way of modulating the envelope so the software actually modulates frequency. It is kind of constant envelope SSB.
Below you can see what the signal looks like. (This is received on a SDR via an attenuator). The signal is a bit too wide. However cool test.
Warning: do not connect the RPI GPIO output running this code to an external antenna without a bandpass or lowpass filter and a valid amateur radio license. Never transmit any signal outside the amateur bands.