- Usha Saha

# Introduction to Signals: A foundation topic for signals and systems

Updated: Dec 15, 2020

A signal is defined as any quantity having information associated with it or a function of one or more independent variables that contains some information. A signal can be a single variable function or multivariable function. The article covers an overview of what is a signal, its various types, basic operations, etc.

Signals are of two types continuous-time signal and discrete-time signals. The continuous-time signal is specified for every instant of time, on the other hand, a signal which is defined for a specific time interval is called discrete-time signals. continuous-time or discrete-time are basically used to represent the nature of the signal with respect to time.

## Types Of Signals

__Basic Signals/ Standard Signals__

These signals are the basic building block of any #complex signal. Basic signals comprise of Step signal, Rectangular signal, Parabolic Signal, Ramp signal, Triangular signal, Impulse function, Exponential signal, Sampling function.

**Basic operations on signals**

** Scaling:- **Scaling can be Time scaling(compression or expansion of signal in the time domain) or Amplitude scaling(compression or expansion of signal in the amplitude).

** Shifting:- **A signal can be shifted in both amplitudes as well as time domain. There are two types of shifting in the time domain, the left shift (also called time advancing), and the right shift(also called time delay). In the amplitude case, the shifting is an upward shift and downward shift.

** Reversal:- **Reversal is a special case of scaling, that reverses the signal. For time-domain, it is called time-reversal, and for the magnitude, it is called magnitude reversal.

There are some other operations also as signal addition, subtraction, multiplication, differentiation, and integration.

**Classification of Signals**

Both continuous and discrete-time signals are classified further as follows. This article deals with continuous-time signal classification.

**Even and odd signals:- **

A signal is said to be an even signal if it satisfies the below condition.

i.e,** ****x(t)=x(-t)** ; for all t.

An even signal is symmetric about the vertical axis. The area under the even signal is two times its one side area.

A signal is said to be an odd signal if **x(t)= -x(-t)** ; for all t. An odd signal is #antisymmetric about the origin. An odd signal must be zero at the origin and the area under the odd signal is also zero. Signals which do not follow the property of even or odd signals are called neither even nor odd signal.

__Periodic and Aperiodic Signals:- __

A** **Signal** **is called periodic if it follows the relation; **x(t+T)=x(t)**; for all t. Here T stands for the period of the signal and a positive constant. A periodic signal repeats continuously over a fixed interval of time, this means it contains all the time ranging from minus infinity to plus infinity. A signal which does not follow the condition of periodicity is called an aperiodic or non-periodic signal.

__Energy and Power Signals:-__

** **A signal is called an energy signal if its total energy is finite** **and** **the average power is zero. In the same manner, a signal is called a power signal if its average power is finite and total energy is zero. The signals that do not come under the power and energy signal category are called neither energy nor power signals(NENP).

Some short cuts to identify energy, power, and NENP signal.

Signals with finite duration and finite magnitude will always be energy signals.

Signals with infinite duration and constant magnitude are always power signals.

All periodic signals are power signals but the opposite is not true.

Signals in which magnitude tends to zero as time tends to infinity are energy signals.

Energy signals are absolutely integrable signals.

__Deterministic and Non-Deterministic Signals:-__

Deterministic signals are functions that are completely specified in time, for these signals nature and amplitude can be predicted at any time. Deterministic signals have a well defined mathematical expression. On the other hand, Non-deterministic signals do not have a well defined mathematical expression that is the pattern of such signal is irregular in nature.

__Causal and Non-causal Signals:-__

A signal is said to be causal if its amplitude is zero for negative time, that is **x(t)=0 for t<0.**

A signal is said to be non-causal if **x(t)** is non zero for **t<0**.** **

A signal is called anti-casual if **x(t)=0 for t>0.**

**Some key points: -**

The concept of continuous-time and analog signal are not the same, an analog signal is not necessarily to be continuous-time.

The concept of discrete-time and digital signal are not the same, a digital signal is not necessarily to be discrete-time.

The Sum of two continuous-time periodic signals may or may not be #periodic.

The Sum of two discrete-time periodic signals is always periodic.

Power and energy signals are mutually exclusive, this implies a signal cannot be both an energy as well as a power signal at a time.

All practical signal is energy signals.

One time differentiation or #integration of an odd signal is an even signal and that of an even signal is an odd signal.