How Does Up-Sampling Work?

[kevin1969]

I have a long history in telecom so I understand the concept of sampling an analog signal and turning it into a digital stream. Perfect example is the early 64K channels in T1's for voice (sample 2x highest frequency and create 8 bit word or each sample (8000Hz * 8 bits = 64K channel).

 

And obviously a digital bit-stream must be sampled at a certain rate to accurately turn it back into analog. But I am confused as to what and how up-sampling works and how it could even create a better quality analog signal from the original digital signal.