How is audio interpolation made?

[Horrible N00B]

I'm trying to see how it works, and want to see if I can use it with an HDMI cable for the GBA portable I'm making. In short, could I make/buy one and slap it onto whatever thing the sound comes out of? If I need to make one, how is it made? If I need to buy one, what do I buy?

 

[Prog]

HDMI is digital. A Gameboy Advance will put out analog sound.
Wait, GBA portable? That's a bit redundant, don't you think?