I had taken a dsp subject during undergraduate course in engineering school. Our lecturer had recommended us a text by Oppenheim et al.- "Signals & Systems", and claimed that the book to be quite informative as introductory text. I don't question that book to be informative, but I doubt it to serve well as an introductory text. For most of us in the class, it definitely doesn't seem to fit as a beginner material, especially we didn't have previous background in signals & systems. If one thinks that, "mathematics" should not meant for understanding an explaination, then most probably he/she would feel difficult to read that book. Same thing go for most of the other signal processing books.
I've passed the dsp exam by gobbling up all the mathematics, but without success in understanding the truths (reasons) behind. Since then, whenever I saw any 'unexplainable' maths to 'explain' a signal process, mostly I would just being frightened away, or even stopped from continue reading it. This certainly couldn't satisfy my desire towards learning new knowledge.
Then, I decided to take a try on this book. Luckily I did. It is indeed the kind of stuff which should be taught in the first place, especially to students (or engineers) who want to learn dsp for the first time, without too much struggling.
This book is understandable, readable, & easy to swallow. Richard Lyons tries avoiding mathematics whenever possible, however if the maths is unavoidable, he will explain it in plain english by giving a "numerical + graphical" example to better visualize it. For example, instead of telling convolution is y(n)=h(k)*x(k), he would further depict the convolution, terms by terms, in the way of y(n) = (1/3) . x(n-2) + (1/3) . x(n-1) + (1/3) . x(n), and putting graphical explaination to aid in better understanding.
If you are looking for a book to start taking off from the land of DSP without prior knowledge on it, no doubt this is one of the best books available. If you are to understand the "reasons" behind dsp in simple way, after learning the maths, like me, this is for sure the first recommendation of all.
After finishing this book, I can't wait to go for other classical books, like the "discrete-time signal processing" by Oppenheim.