• Signals and Systems
• Requirements for Linearity
• Static Linearity and Sinusoidal Fidelity
• Examples of Linear & Nonlinear Systems
• Special Properties of Linearity

• Superposition: the Foundation of DSP
• Common Decompositions
• Alternatives to Linearity
• Summary of the key concepts

Most DSP techniques are based on a divide-and-conquer strategy called superposition. The signal being processed is broken into simple components, each component is processed individually, and the results reunited. This approach has the tremendous power of breaking a single complicated problem into many easy ones. Superposition can only be used with linear systems, a term meaning that certain mathematical rules apply. Fortunately, most of the applications encountered in science and engineering fall into this category. This chapter presents the foundation of DSP: what it means for a system to be linear, various ways for breaking signals into simpler components, and how superposition provides a variety of signal processing techniques.