This subject is huge, but to keep it very brief, it basically means putting digitised audio, say some songs of yours, into a computer. There are a few different stages of digital processing, listed below.
Converting analogue sound signals to digital - and sending this information to a computer's hard drive. This really needs good gear with fine converters. For simplicity, let's refer to all the digitised stuff as tracks.
Mixing the songs is the next stage - playing all the tracks in the right order, editing them if needed, sending them to effects.
The next type of processing - effects. This is where you can manipulate the songs to change, say, the volume and tone of a vocal track. You could add incredibly real reverberant spaces from cathedrals to studios and woodland. Change a voice's pitch and timing for creative reasons (and correct pitch and timing anyway, if it's wrong). GrungeUlize guitars. Add synths and samples - and such as EQ (tone), reverberation, and some of the more odd-souning effects such as chorus, envelope-follower, vovoder, etc: Whatever seems right.
After all this mixing, there's still usually the need for mastering the finished CD, with final tweaks for tone and loudness. Adding some 'space' on a track, maybe. Assembling the tracks in the correct order. Getting the relative loudness of all the tracks to work well together, and making ther tracks flow, with the right pauses.
And Finally . . . burning the CD master-disk (or any other format required by a pressing-plant) to send to the pressing-plant. Then, back at home, your songs are converted to analogue signals in your CD player/sound system - So make sure it's a good one, or you won't get the full benefit off all our fine work!
Pssssstt! . . . We can also use some great analogue gear, so this involves converting from digital, to analogue, processing with the analogue gear - compressor, or EQ - and then digitising again. Of course, the analogue gear can be used 'on the way in', to warm up some sounds, if necessary.
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