# Signals and Systems/Definition of Signals and Systems

## Signals[edit]

What is a signal? Of course, we know that a signal can be a rather abstract notion, such as a flashing light on our car's front bumper (turn signal), or an umpire's gesture indicating that a pitch went over the plate during a baseball game (a strike signal). One of the definitions of signal in the Merrian-Webster dictionary is:

"A detectable physical quantity or impulse (as a voltage, current, or magnetic field strength) by which messages or information can be transmitted." or

"A signal is a function of independent variables that carry some information." or

"A signal is a source of information, generally a physical quantity, which varies with respect to time, space, temperature like any independent variable" or

"A signal is a physical quantity that varies with time, space, or any other independent variable by which information can be conveyed"

These are the types of signals which will be of interest in this book. We will focus on two broad classes of signals, *discrete-time* and *continuous-time*. We will consider discrete-time signals later. For now, we will focus our attention on continuous-time signals. Fortunately, continuous-time signals have a very convenient mathematical representation. We represent a continuous-time signal as a function *x(t)* of the real variable *t*. Here, *t* represents **continuous time** and we can assign to *t* any unit of time we deem appropriate (seconds, hours, years, etc.). We do not have to make any particular assumptions about *x(t)* such as "boundedness" (a signal is bounded if it has a finite value). Some of the signals we will work with are in fact, not bounded (i.e. they take on an infinite value). However most of the continuous-time signals we will deal with in the real world are bounded.

Signal: a function representing some variable that contains some information about the behavior of a natural or artificial system. Signals are one part of the whole. Signals are meaningless without systems to interpret them, and systems are useless without signals to process.

Signal: the energy (a traveling wave) that carries some information.

Signal example: an electrical circuit signal may represent a time-varying voltage measured across a resistor.

A signal can be represented as a function x(t) of an independent variable t which usually represents time. If t is a continuous variable, x(t) is a continuous-time signal, and if t is a discrete variable, defined only at discrete values of t, then x(t) is a discrete-time signal. A discrete-time signal is often identified as a sequence of numbers, denoted by x[n], where n is an integer.

Signal: the representation of information.

## Systems[edit]

A **System** is any physical set of components that takes a signal, and produces a signal. In terms of engineering, the input is generally some electrical signal X, and the output is another electrical signal(response) Y. However, this may not always be the case. Consider a household thermostat, which takes input in the form of a knob or a switch, and in turn outputs electrical control signals for the furnace.

A main purpose of this book is to try and lay some of the theoretical foundation for future dealings with electrical signals. Systems will be discussed in a theoretical sense only.