In many cases, we are presented with a specific system and are interested in characterizing it in detail to understand how it will respond to various inputs. In another context, our interest may be focused on the problem of designing systems to process signals in particular way. Analysis of a system is investigation of the properties and the behavior (response) of an existing system. Design of a system is the choice and arrangement of systems components to perform a specific task. Design by analysis is accomplished by modifying the characteristics of an existing system. Design by synthesis means that we define the form of the system directly from its specifications.