The dsPIC's are pretty good general purpose micro-controllers (it's just the usual PIC core), I've no idea how they are as DSP's though? - I keep meaning to have a play with one.One example is to record all 4 signals for 10,000 samples then go back and process them in NOT-real time.
There are DSPs that probably can do that in real time. Could use 4 small DSP parts.
A DSP is made to do this job, but is not a good microcontroller for general purpose applications.