There actually is full fledged t.38 support for asterisk: http://www.attractel.com/faxterisk.php
2 week trial licenses are available.Also have a look at our zoiper softphone which can receive, and in the next version, somewhere next week also transmit faxes over t.38.
I checked out the Faxterisk commercial software solution and it seems like a good T.38 solution for Asterisk. Here's how it works: a fax terminal passes analog data to a T.38 gateway. The gateway takes the signal, demodulates it and transmits it over the existing IP network to another T.38 capable device(e.g. Internet Aware Fax(IAF) or a compatible Analog Telephone Adapter (ATA) or another T.38 gateway that modulates back the digital signal and sends it over the PSTN to another fax terminal.
Faxterisk bold claims, "The sensational part of our Faxterisk solution is that it is actually a far more reliable faxing method than traditional analogue faxing. This is not a phenomenon; it is due to the fact, we may want to believe that landlines are good carriers, but this is far from true as far as greater distances are concerned. IP networks are more reliable carriers over long distances and with our FoIP solution, you will inevitably enjoy faxing more than ever!"
The Faxterisk package includes:
T30faxRX for receiving normal faxes over PSTN
T30faxTX for transmitting normal faxes over PSTN
T38faxTX for T.38 fax origination (IAF fax)
T38faxRX for T.38 fax termination (IAF fax)
T38gate for FoIP gatewaying
You don't even have to change anything in your dialplan. Basically, Faxterisk auto-detects the fax signal and automatically switches to fax mode. I should mention that Faxterisk works with Asterisk 1.4.X versions only. It supports the following ITU-T modems: V.27ter, V.29 and V.17 with speeds of up to 14400 bps.
Alternatively, Spandsp adds integrated faxing capability to Asterisk via some GPL patches. Spandsp is a library for Digital Signal Processing(DSP) which is used to turn images into fax tone audio signals and back. You can look at this instruction link and the download link for some help installing. Spandsp only supports V.29/9600bps due since higher speed modems for fax are encumbered by patents. spandsp implements only unencumbered standards, so it may be distributed freely.