This textbook gives a fresh approach to an introductory course in signal processing. Its unique feature is to alternate chapters on continuous-time (analogies) and discrete-time (digital) signal processing concepts in a parallel and synchronized manner. This presentation style helps readers to realize and understand the close relationships between continuous and discrete time signal processing, and lays a solid foundation for the study of practical applications such as the analysis and design of analogies and digital filters. The compendium provides motivation and necessary mathematical rigor. It generalizes the Fourier transform to Laplace and Z transforms, applies these transforms to linear system analysis, covers the time and frequency-domain analysis of differential and difference equations, and presents practical applications of these techniques to convince readers of their usefulness. Matlab examples are provided throughout, and over 100 pages of solved homework problems are included in the appendix.