Signals and systems

This text assumes a basic background in the representation of linear, time-invariant systems and the associated continuous-time and discrete-time signals, through con­ volution, Fourier analysis, Laplace transforms and Z-transforms. In this chapter we briefly summarize and review this assumed background, in part to establish no­ tation that we will be using throughout the text, and also as a convenient reference for the topics in the later chapters. We follow closely the notation, style and presen­ tation in Throughout this text we will be considering various classes of signals and systems, developing models for them and studying their properties. Signals for us will generally be real or complex functions of some independent variables (almost always time and/or a variable denoting the outcome of a proba­ bilistic experiment, for the situations we shall be studying). Signals can be: 1-dimensional or multi-dimensional • • continuous-time (CT) or discrete-time (DT) • deterministic or stochastic (random, probabilistic) Thus, a DT deterministic time-signal may be denoted by a function x[n] of the integer time (or clock or counting) variable n. Systems are collections of software or hardware elements, components, subsys­ tems. A system can be viewed as mapping a set of input signals to a set of output or response signals. A more general view is that a system is an entity imposing constraints on a designated set of signals, where the signals are not necessarily la­ beled as inputs or outputs. Any specific set of signals that satisfies the constraints is termed a behavior of the system.