2002 Ford Focus SVT Shaking Troubles

My 2002 Focus SVT seems to be having trouble lately.

It began with it shaking towards the end of 3rd and sometimes 4th gear, but now the shaking appears sporadically in every gear.

It happens most often after a cold start, but can even appear lately at any time.

During these shakes, regardless of speed or gear, if I let off the gas the car stalls 50% of the time.

If I press the gas further, the shaking intensifies but the vehicle within approximately 10 seconds will "pull itself out of it" and resume normal operation until the next incident, which can be as short as a few seconds to as long as an hour or more.

Any ideas?