As someone who is pure CS who hated EE, I now work in an EE shop as the only programmer performing most of the PC based DSP work, and the only thing I would recommend is this, http://www.dspguide.com/pdfbook.htm.

And of course: http://mri-q.com/uploads/3/2/7/4/3274160/quad_signals_tutori...

I found Richard Lyons' book an even better introduction. http://www.amazon.com/Understanding-Digital-Signal-Processin...

I'll trade jobs with you (I'm an EE doing NLP) :P

That is a good book. I personally have it bookmarked.

My first 'professional' programming gig was at an RF shop building software defined radios. I was programmer #2 and the DSP Guide absolutely saved me when I first got on board there. As another comment author said, it is also one of the best technical books I've ever read.

I second this. Honestly one of the best technical books I have ever read.

More introductory DSP for non-EE people:

http://jackschaedler.github.io/circles-sines-signals/

http://dsp.cs.cmu.edu/

That is awesome, thanks. (Gilbert Strang is awesome.)