E, welcome to the forum!
Decoding those formats is one thing, and listening to them is another.
A PC sound card can decode both formats (I have a Creative Audigy card from 2004 that does them just fine) and so can most newer home theater receivers. However, you'll need speakers and some sort of amplification to drive the speakers. A receiver will give you that amplification, so you'll want one of those unless you have or plan to buy some other amp. A PC sound card, while it can decode those formats, can't power your speakers.
Can you tell us any more about your system? We could help you out better if we knew how you plan to listen to DD and DTS. Thanks.
Adam