Conexant HCF & HSF modems aren't "true" modems, in the sense that all the tone generation and signal processing is done in software by the drivers, rather than in hardware on the modem board as a traditional modem will do. Therefore you need specialised drivers for the modem.
Conexant don't produce drivers for Linux (I have an HSF modem - I had the same problem as you), but if you check out
http://www.linuxant.org you'll find they have created Linux drivers for HCF and HSF modems. The free version limits you to 14.4kbps, but it will let you test whether the drivers will work with your modem. If they do, you'll probably want to get the full drivers - they're not very expensive, only £9 or so ($15).