- easy to read and understand

- accurate formulae and no conceptual errors (surprisingly, I've come across a number of books in which the author has made major conceptual errors, or obvious mathematical mistakes!) This can be very counterproductive for someone attempting to learn the material for the first time.

- concise, useful information without all the pointless 'exercises' and irrelevant fluff which can balloon a small text to preposterous length.

- contains hard-to-find or specialized information

- are very cheap/free and readily available

A cautionary note for those who havn't touched DSP theory before: I don't want to scare anyone off, but some of this material gets highly theoretical, and a university level mathematics education will come in very handy, and in some cases is essential. Many of these books contain good primers on the necessary math, but may still rely on a solid undergraduate level foundation of calculus, linear algebra and differential equations. Much of DSP theory stands on complex mathematics, and a conceptual understanding of the equations goes a long way. Also very useful is some basic signal theory. You should know what an impulse is (conceptually and mathematically), and what the impulse response is. Convolution is a good concept to know, and some knowledge of transfer functions doesn't hurt either.

That said, I encourage everyone to have a peek anyway because while the equations and some of the concepts may seem completely abstract, one can still gain a great deal from the explainations and diagrams etc... so, here we go:

1. "Understanding Digital Signal Processing" by Richard G Lyons. ISBN 0201634678

This is definitely my favorite book on DSP. No other DSP author I've read has the ability to explain difficult abstract topics as clearly, concisely, and correctly as Mr. Lyons. The book doesn't deal specifically with audio too much, but does include a very enlightening discourse on complex math as it relates to DSP. And to put the cherry on the cake, it's reasonably priced by comparison to other DSP texts. My #1 recommended read!

2. "Digital Signal Processing Using MATLAB" by Ingle & Proakis. ISBN 0534371744

This one's really helpful for testing filters in MATLAB. One thing I really like about digital audio is that most of the time, a simulation is exactly the same as the real thing, unlike a SPICE simulation of an analog circuit where the real-world implementation may contain some hidden surprises.

3. "Digital Audio Signal Processing" by Udo Zolzer. ISBN 0471972266

Ok, this one contains some highly theoretical stuff, but for those who already have a solid understanding of DSP, it's an invaluable resource of info you won't find anywhere else.

4. http://www.dspguide.com/ - there's a free book here (yes free, all 640-odd pages!). I havn't read it all, but from a brief browse, it looks ok. You can't go wrong with free...

OK, happy reading people!