# Signals and Systems/Definition of Signals and Systems

## SignalsEdit

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"

As per a new definition of signal proposed in- Pragnan Chakravorty, "What Is a Signal? [Lecture Notes]," IEEE Signal Processing Magazine, vol. 35, no. 5, pp. 175-177, Sept. 2018. doi: 10.1109/MSP.2018.2832195:

"A signal, as a function of one or more variables, may be defined as an observable change in a quantifiable entity"

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.

## SystemsEdit

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.