It would help if you tell us EXACTLY what you're trying to do...
Technically, I have little experience with the software that powers digital audio processing and as much practical experience as just having spent time as an amateur musician who has seen a lot of guitar pedals and effects in action.
DSP is an advanced programming topic. If you were studying university computer science or engineering it's probably a 4th year class. There is a [u]free online DSP book[/u] if you want to look into it.
And, the Arduino is not really powerful enough for any "serious" audio processing (although some people have made guitar pedals).
Most guitar pedals are analog. Some are digital, and some things (like delay) can be done digitally without a processor.
I wouldn't recommend real-time audio processing on a regular computer either. It can be done but the multitasking operating system means you need input & output buffers, and buffers are delays. People who do real time audio through a computer often struggle to get the latency (delay) down to an acceptable level.
I know that there are Shields out there that are specialized for audio application.
Most of these shields have all of the electronics for playing an audio file. There's memory, a clock, and a digital-to-analog converter. The Arduino isn't even "seeing" the audio, it's just selecting a file and starting/stopping playback (and maybe volume control or some other control-inputs to the audio shield).
I actually would be interested to learn about different ways to process digital signals for a live audio application, if that makes sense.
Get an audio equalizer or other [u]effects processor[/u]. (These usually process analog audio, even if they are digital internally.)
Alternatively, a better question would be what are the practical uses of digital signals for gathering raw data to support programs on the Uno designed to perform diverse functions not limited to audio output
The Arduino can do things like sound activated lighting. I've made some sound-activated lighting effects with the Arduino. The effects I've made only depend on "loudness", but you can do some frequency analysis in hardware or software. For my effects, I use a circuit called a peak detector, that puts-out a varying DC voltage that follows the peak signal level... That way my Arduino can sample the "loudness" slowly (about 10 times per second) and I don't have to read or "process" the actual audio signal.
If you want to do frequency analysis in software, there are Arduino libraries for that, so you don't have to do all of the DSP programming yourself.