I want to develop a FAX application.I searched on google and found some links ,applications for developing FAX apps on android.But I want to develop application using native app
The fax communication option is embedded in GSM protocol since the very beginning, it's natural by design. Is uses optional GSM data tranfer protocol for fax transmission, so it was lame to say that GSM audio quality isn't good enough.
There's no analogue demodulation when fax goes over GSM network, it converts to digital on entering provider's PBX.
Get an old good Nokia 9500 it had implemented Symbian-based fax application by default, that worked perfect on any GSM-provider. On some providers, you needed to enable an additional phone number for receiving facsimile messages, on some phones like Siemens M55 you could receive fax by clicking a menu option on any incoming call even by main cell line.
I think Google is responsible for providing users with an appropriate GSM faxing software for free, as most of the mobile manufacturers did before. Everything present on play market by search 'fax' or 'facsimile' is junk.
P.S. There is also a special protocol for fax transmission on VoIP lines, it's T.38 or G.711 pass-through; if your provider/nodes and hardware supports one of those you are lucky to send and receive faxes over internet connection as well. Eg. my own working set of hardware is Brother 9440/Planet VIP-156/sipnet.ru.