This text relies on graphics, the language of scientists and engineers, for the physical interpretation of subtle mathematical concepts. It establishes a solid background in Fourier, Laplace, and z transforms, before extending them in later chapters. The author presents a unique matrix-equation-matrix sequence of operations that dispels the mystique of the fast Fourier transform, explores the application of digital signal processing technology to real-time processing, and introduces his own generalization of the Dirac-delta impulse and distribution theory. He also offers extensive referencing to MATLAB(R) and Mathematica(R) for solving the examples.