Elements of Acoustic Phonetics

It was a joy to see very complicated concepts (e.g. LMS for LPC analysis) explained so simply and naturally. Close to no math prerequisites for this one, if that's your concern. If you do get lost, the author's crystal clear prose and explainations are going to come back and pick you up, and even if you miss a technicality, it doesn't matter because you will understand the big picture and the practical applications. (Which incidentally is exactly the opposite of what happened during my studies at University.)
This was my first book in this field and I found it very insightful. I'm coming from a theoretical background in DSP, and yet I wasn't bored at all by the step-by-step mathematical derivations.

Major improvements are using the source-filter in place of spring resonance model and fine tutorials on digital speech processing. An excellent first text for the student phonetician. For more advanced students use my 1999 text. J.M. Pickett.