Push To Talk (PTT) 0n Arduino

Hi, There are a number of applications that allow for PTT communications on smartphones running on Android and Apple OS. As a project, I would like to create a PTT application using an Arduino to control a GSM modem and a simple 1 or 2 line LCD. The audio side of things (mic and speaker) could either be controlled by the Arduino or the GSM modem. I was wondering if anyone on the forum can point me in the right direction. I have had a fair amount of success using the Arduino to control a GSM modem for telemetry, but have never ventured into the arena of audio or PTT. Any assistance would be greatly appreciated.

I don't think (correct me if im wrong guys) an arduino has the processing or memory power required for processing audio in such a manner. Surely that would be a job for a beagle or pi