Re: New to DSPs
DSP chips used to be micros on steroids, now the difference is not so great as far as processing speed is concerned. A lot of DSP from the old days (56001)can be done on the newer 32b chips. The important differences are the specialised instructions including MAC for common functions used in dsp algorithm implementation and usually a Harvard architecture.
What sort of DSP do you want to know? If you want the full theory, the standard texts are nearly all called something like Discrete time signal processing or Digital Signal processing and some authors to look for are Rabiner and Gold, Oppenheim and Schefer. DSP is also used in control systems and a good book for that is Ogata Discrete time control systems.
If you just want to play with music and digital filters from a hobby point of view without doing all the maths then Musical applications of microprocessors by Chamberlin is a good introduction although a bit old now.
The application notes from the DSP ship makers are probably the best to start reading.
DSP is a vast and complex but rewarding area of work - good luck.