INTRODUCTION TO BASIC SIGNALS
1. Introduction
• Signal is considered as a function of time that represents a physical variable associated with a
system.
• In electrical systems: signals usually represent currents and voltages
• In mechanical systems: signals represent forces, velocities, positions, pressure, acceleration
• Definition of signal – any physical quantity that varies with time, space or any other
independent variable or variables
2. Basic Signals
Basic signals or elementary signals can be used as basic building blocks for the modelling of
more complicated signals. To study the response and behaviour of systems the basic signals are
used as inputs. Some of the basic signals are impulse, step, ramp, parabolic, exponential, and
sinusoidal signals.
1. Sawtooth and square function
The sawtooth function generates a sawtooth wave with peaks at ±1 and a period of 2π. An optional
width parameter specifies a fractional multiple of 2π at which the signal's maximum occurs.
The square function generates a square wave with a period of 2π. An optional parameter specifies duty
cycle, the percent of the period for which the signal is positive.
Generate 1.5 seconds of a 50 Hz sawtooth wave with a sample rate of 10 kHz. Repeat the computation
for a square wave.
2. Sinusoidal signal
The fundamental period of the signal x(t) is
3. Unit impulse function: δ(t)
This signal is considered as one of the elementary signal and plays an important role in the signal
analysis. It is defined as
1
Thus δ(t) is zero everywhere except at t=0, and the total area under unit impulse is unity. This
function is also called as Dirac-Delta function
The unit impulse δ(t) is considered as the limiting form of a rectangular pulse of unit area. Consider
the rectangular pulse shown below
Consider the rectangular pulse with unit area. If the duration of the pulse is decreased and its
amplitude is increased such that the area under the pulse is maintained constant at unity. As the
duration of the pulse decreases, the rectangular pulse approximates the impulse.
4. unit step function: u(t)
The unit step function is defined as,
The function has a discontinuity at t=0, since the value of u(t) changes instantaneously from 0 to 1
when t=0
5. unit ramp function: r(t)
The unit ramp function is defined as
2
The term unit refers to the slope of the line.
6. Exponential signal:
A real exponential signal is defined as
Where, A is the amplitude of the signal at t=0 and a is a constant.
Depending on the parameter, a two types of real exponential signals are defined:
- Decaying exponential for a < 0
- Growing exponential for a > 0
If a = 0, the exponential signal reduces to a dc signal.
