What is a Unit Step Signal?

What is a Signal?

A signal is defined as a single-valued function of one or more independent variables which contain some information. Examples of signals are electric current and voltage, human speech, etc.

Unit Step Signal

The step signal or step function is that type of standard signal which exists only for positive time and it is zero for negative time. In other words, a signal x(t) is said to be step signal if and only if it exists for t > 0 and zero for t < 0. The step signal is an important signal used for analysis of many systems.

If a step signal has unity magnitude, then it is known as unit step signal or unit step function. It is denoted by u(t).

The step signal is equivalent to applying a signal to a system whose magnitude suddenly changes and remains constant forever after application. If we want to obtain a signal which start at t = 0, so that it may have a value of zero for t < 0, then we only need to multiply the given signal with the unit step signal u(t).

In practice, the unit step signal is used as a test signal because the response of a system for the unit step signal gives the information about how quickly the system responds to a sudden change in the input signal.

Continuous-Time Unit Step Signal

The unit step signal which is defined for every instant of time is known as continuous-time unit step signal. The continuous-time unit step signal is denoted by u(t).

Mathematically, the continuous-time unit step signal u(t) is defined as follows −

$$\mathrm{u(t)=\left\{\begin{matrix} 1\; \; for\; t\geq 0\ 0\; \; for\: t< 0\ \end{matrix}\right.}$$

From the above definition of the continuous-time unit step function, it is clear that the unit step function is zero, when the time (t) is less than zero and when the time (t) is greater than or equal to zero, then u(t) is unity.

The graphical representation of the continuous-time unit step signal u(t) is shown in Figure-1.

Discrete-Time Unit Step Signal

The unit step signal which is defined only at discrete instants of time is known as discrete-time unit step signal. It is denoted by u(n). Mathematically, the discrete-time unit step signal or sequence u(n) is defined as follows −

$$\mathrm{u(n)=\left\{\begin{matrix} 1\; \; for\; n\geq 0\ 0\; \; for\: n< 0\ \end{matrix}\right.}$$

The graphical representation of the discrete-time unit step signal u(n) is shown in Figure-2.