Using a microcontroller (which is a microprocessor with extras like clocks, A/D, D/A(sometimes) and some exernal parts and controls the job can be done. The software creation is best done with an emulator, these can be a bit pricy. For a simple job, an 8 or 16 bit microprocessor would do the job well. Many 16 bit micros are tailored to this kind of job. 68HC11 OR 'HC12, or a 8051 varient would be good.
Sean