How to test existing digital handsets with Asterisk?

We are using Avaya with digital handsets at work. If I wanted to test these handsets with an Asterisk setup at home (I have Time Warner Cable phone service), how can I test digital handsets if I have analog at home? What hardware do I need?

Are they digital or SIP?

They are the Avaya 4412d+ digital phones.

If they are not SIP, the main piece of hardware you will need is an Avaya PABX.