There are digital signal processors. They have A/D and D/A. Audio goes in, gets digitized, effected, coverted to analog and comes back out. That is not how DAWs work. A recorded file is purely digital in a DAW. Nothing will change that digital representation unless the software instructs it to.
Of course it is purely digital. Everything in a digital computer is digital,
including the audio signal I referred to. It is in the form of a stream of numbers, but it is an audio signal none the less. Just like the ones that flow through SPDIF cables.
The digital audio stream flows through the plug-in, as I said, which performs DSP operations on it.
DSP has its roots in astronomy, where the movement of celestial bodies could be monitored and calculated.
DSP could be deployed on a humble Z80 2MHz processor, but only for signals very much lower in frequency than multitrack audio.
You could perform all of today's DAW plug-in DSP operations with just a pencil, notepad, and pocket calculator. Just not in real time.
DSP chips were developed, to specialize in performing tight repetative algorithms, on data streams.
What is absolutely amazing is that general purpose processors, like those used in PCs have developed so far from where they started,
that they are now capable of performing real-time DSP operations on multi-tracks of audio.
It is this advanced capability that has led to DAWS being possible, and sophisticated plug-ins being able to be added to them.
The plug-in will set up some data srtructures, and then operate in a tight loop applying its DSP algorithm to the digital audio stream passing through it, and
produce a new digital audio stream being the processsed result.
Plug-ins are all about number-crunching the digital audio stream.
Going back to my first post, the digital audio stream IS the audio signal.
I do not see a real difference between electrical analogue audio, and the sampled digital audio stream.