This book is the basis for Instructor Rick Lyons' course, DSP: Understanding Digital Signal Processing from Besser Associates.
From the publisher:

This is undoubtedly the most accessible book on digital signal processing available to the beginner. Using intuitive explanations and well-chosen examples, this book gives you the tools to develop a fundamental understanding of DSP theory. The author covers the essential mathematics by explaining the meaning and significance of the key DSP equations. Comprehensive in scope, and gentle in approach, the book will help you achieve a thorough grasp of the basics and move gradually to more sophisticated DSP concepts and applications.
The book begins with a complete explanation of the often misunderstood topic of periodic sampling. The introduction to the important discrete Fourier transform, and its fast Fourier transform (FFT) implementation, is the most lucid and illuminating explanation available anywhere. You will also find extensive information on both finite impulse response (FIR) and infinite impulse response (IIR) digital filters, as well as coverage of the benefits of signal averaging. In addition, the book demystifies the abstruse topics of the Convolution theorem and complex signals. The practical uses of various binary number formats are also carefully described and compared. Finally, a collection of tricks-of-the-trade used by professionals to make DSP algorithms more efficient will help you apply DSP concepts successfully.