Built in DSP = digital equalizer?

Hi, could you elucidate what DSP does, like for example the Wadia Digimaster software? Is it in fact a sort of equalizer that alters the frequency content of music signal so music has less of a mechanical and harsh quality, which is typical of digital music reproduction? If it is true that DSP alters the sound characteristics it is not a puristic way of signal reproduction...

A digital signal processor is just that. I takes in data processes/transforms it according to a program (usually firmware) and outputs the result.

If the program is to work as an equalizer, it is an equalizer. If the program is to decode DolbyTrueHD into PCM, it is a decoder. If the program is to analyze room acoustics when fed from a microphone input, it is an analyzer.

How transparent it is depends on many, many variables but there is no reason why, given a digital signal, the DSP cannot be subjectively transparent.

I don't think DSP necessarily mean digital equalization. It simply means digital processing which is used in the Wadias to perform precision upsampling and volume control. DSP is not used in the Wadias to equalize the frequency response but is used to facilitate D/A conversion.
It's my understanding that DSP is any signal processing that occurs in the digital domain.

On the other hand, some manufacturers tend to use DSP as though it's a proprietary term for whatever process they may be using, so for a lot of end users, it connotes what their equipment does in terms of DSP.

As an example, I have several pieces of Meridian gear. One is a 518 which is a digitial-to-digital processor for upsampling, volume control, filtering, etc. Another is my 565 is decoding formats (like DD, DTS, etc.), has embedded soundfield options (Trifield, Chamber, etc.), controls volume, tone, delay, polarity and some other odds and ends. The digital speaker can also perform some processing such as bass, treble, tilt, room boundary compensation, etc.) IMHO, they are all DSPs, but with different functionality.

Clear as mud?
Not all the CD player manufacturers use DSP. Wadia was the first one who uses DSP (Digimaster software). I think the manufacturers of 16 bit non-oversampling CD players/DAC's don't apply any DSP. Btw, is DSP a good thing? How much signal manipulation is needed for CD to sound good?

I don't think there's a rule to how much DSP is needed for cd to sound good. The only problem with DSP is that it might smear the time responses of the digital signals. However, if carefully implemented the effect will be minimized or even reversed.