Does anyone know of any straightforward books/PDFs/what-have-you that give a grounding in DSP math accessible to someone with a strong background in programming and first-year calc? I'm really interested in the mathematics behind a lot of these audio concepts that I've read about, and I want to formulate and play around with a few ideas that occur on me from time to time.

The less they cost, the more they're preferred, as always.

Not exactly what you're looking for, but have you looked at this site? http://www.musicdsp.org/ It may help.

1st yr calculus i fink wont help with DSP
it don't even talk about fourier transfrom and frequency domain ananlysis.
if you have done signal processing or at least engineering maths b4 they would do some help.

I think his point was that he wanted to learn about things like that, and was giving his level of current knowledge. To that end, first-year calculus is sufficient, engineering math itself (especially DSP) is generally fairly elementary as far as math goes (just basic calculus); it's the various impliciations of the mathematically-simple formulae and their interactions that are complex.

Could definitely be a place to start. Thanks for the link.

@Delirium: That's more or less what I thought it'd be like and how I feel. I'm willing to put the work in to get myself to a reasonably fluent level.

a google search result for "dsp online book"
http://www.dspguide.com/pdfbook.htm

Now is a good time to go to whatever the closest engineering college has for a used book exchange.
If you're lucky, whatever book they are using for a DSP or communications systems course
is being replaced next year and the old ones would then go for cents on the dollar.
Also look for a linear algebra book which should cover Taylor series and Fourier Series type of stuff..
In my day they wouldn't have had a separate course on digital audio as the phone company and
military were probably the only ones using it.

Try Schaum's outline on Digital Signal Processing. It costs about $16 on Amazon and is fairly straightforward.

Maybe I'll twist this around to make it a little more personal:

Where did you all gain your knowledge of DSP math from?

Mostly at school. And I did work for 6 years in a department called "Sensor and SIgnal Processing" at GE's research center, but never on an audio project.

These are both generally introduced in Calc II. I know taylor series are covered in a lot of detail . . . its basically all thats in the AP Calc BC exam. I haven't taken linear yet, so maybe they are covered there as well ?

Yeah, Taylor series are generally a high school calculus type thing. Some DSP-related stuff might be in a linear algebra class, depending on how it's taught (knowing about linear transformations might be useful, for example), but most of linear algebra is really completely unrelated stuff -- vector spaces, eigenvectors, Banach spaces, etc.

Well, it's technically actually quite closely related, but more from a theoretical standpoint than from a practical one -- if you want to derive Fourier theory, a knowledge of linear algebra will be indispensible (for example, Hilbert spaces provide a convenient way to formalize and generalize a Fourier transform). If you just want to use already-established theory (that is, you're looking to implement or understand software or hardware, not to write papers for mathematics journals), then simply picking up a DSP textbook (which mostly is understandable with high-school-level math) will be more useful.