# What is Signal? Types with Classification, Examples & Operations

Hi Friends! Today, here we will explain about what is signal; involving with different types of signal with Classification, examples and operations with ease. After reading this content, you will be getting fully educated about What is Signal & Types without getting any hindrance.

## Signal Definition

Signal is any physical quantity that varies with one or more independent variables, such as time, spatial coordinates, or intensity of colors. They can be continuous-valued (analog) or discrete-valued (digital). Signals are usually represented as functions of their independent variables, such as x(t) for continuous-time signals or x(n) for discrete-time signals.

Single variable signal is a function of the single independent variable, such as time. Examples of one-dimensional signals include music, speech, and heartbeats. The value of a signal at any specified value of the independent variable is called its amplitude, and the sketch of the amplitude of a signal as a function of the independent variable is called its waveform.

Two-variable signal is a type of signal that is a function of two independent variables. Mathematically, it can be represented as X(p, q) = 0.6p + 0.5q + 1.1q^2, where the signal varies with the independent variables p and q. Examples of signals that vary with two independent variables include images and certain physical phenomena.

## ‘What is Signal’ Tutorial Headlines:

1. Signal Definition
2. Classification of Signals
• On the Basis of Type
• On the Basis of Time
• On the Basis of Variables
• On the Basis of Nature
• On the Basis of Behaviour
• On the Basis of Symmetry
1. Different Types of Signals with Examples
• Analog Signals
• Digital Signals
• Continuous-Time Signals
• Discrete-Time Signals
• One Dimensional Signals
• Multidimensional Signals
• Periodic Signal
• Aperiodic Signal
• Deterministic Signals
• Random Signals
• Even Signal
• Odd Signals
• Energy and Power Signals
• Causal and Non-Causal Signals
• Real and Imaginary Signals
1. Basic Operations of Signal
2. Applications of Signals in Real Life
• What is a signal in electronics?
• What is the purpose of signals in communication?
• How are signals classified?
• How many types of signal with examples?
• What is the difference between analog and digital signals?
• How are signals used in communication systems?
• What is the role of signals in control systems?
• How are signals represented mathematically?
• What are transients in signals?
• How are signals processed in digital systems?

## Classification of Signals

Signals can be classified into various categories based on their properties and characteristics, including:

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• On the Basis of Type
• On the Basis of Time
• On the Basis of Variables
• On the Basis of Nature
• On the Basis of Behaviour
• On the Basis of Symmetry

Further in this article, all these things will be explained in detail along with their suitable examples.

## Different Types of Signals with Examples

Here, we will try to cover some common types of signals along with examples; below shown each one, you can check them:

## On the Basis of Type

### Analog Signals

Analog signals are continuous-time signals that represent some other quantity, such as sound, light, temperature, or pressure. They continuously and infinitely vary in accordance with some time-varying parameter.

### Examples of Analog Signals

• Television Waves: Older televisions used analog signals to display images and sound.
• Sound Waves: The human voice and music are natural analog signals, as the sound pressure varies continuously.
• Voltage and Current: These are examples of analog signals in the electrical domain, as they continuously change in amplitude and frequency.
• Frequency: The frequency of a signal can also be an analog signal, as it varies continuously over time.

### Digital Signals

Digital signal is a representation of data as a sequence of discrete values at any given time, unlike an analog signal, which represents continuous values. It is an abstraction that is discrete in time and amplitude, with the signal’s value only existing at regular time intervals. Digital signals are binary in nature and can only take on a finite number of values, typically represented as square waves.

### Examples of Digital Signals

Communication Systems: Digital signals are commonly used in communication systems for data transmission over point-to-point or point-to-multipoint channels.

Control Systems: Digital signals are used in control systems with devices such as digital input modules, which capture and digitize signals from switches, sensors, or transducers.

## On the Basis of Time

### Continuous-Time Signals

Continuous-time signal is a type of signal whose amplitude is defined for every point in time within a specified time interval. In other words, it is a signal that varies continuously over a continuous range of time. Continuous-time signals are typically represented by mathematical functions.

Mathematically, a continuous-time signal x(t) is a function of time t, where t can take on any value within a specified interval. The signal x(t) is defined for all real values of t in that interval. The amplitude of the signal can take any value at any given instant in time.

### Examples of Continuous-Time Signals

Analog Audio Signals: The variations in air pressure that create sound waves are continuous-time signals. When you speak or play a musical instrument, the resulting sound wave is a continuous-time signal.

Analog Voltage Signals: In electronics, the voltage across a capacitor or resistor in an analog circuit can be a continuous-time signal. For example, the output voltage from a continuously varying sensor, like a temperature sensor, can be represented as a continuous-time signal.

Continuous-Time Sinusoidal Waves: x(t)=Acos(2πft+ϕ), where A is the amplitude, f is the frequency, t is time, and ϕ is the phase, represents a continuous-time sinusoidal wave. Such waves vary smoothly and continuously over time.

### Discrete-Time Signals

Discrete-time signal amplitude that is defined at distinct and separate points in time. In other words, it is a signal that varies only at specific discrete instances in time. Each sample of the signal is associated with a specific time instant, and there is no notion of amplitude between these sample points.

Mathematically, a discrete-time signal x[n] is represented by a sequence of values, where n is an integer index corresponding to the discrete time instances. The sequence can be infinite or finite, depending on the context. Discrete-time signals are often encountered in digital signal processing and digital communication systems.

Examples of discrete-time signals include the unit step function, which is defined as u[n] = 0 for n < 0 and u[n] = 1 for n ≥ 0, and the impulse function, which is a delta function centered at time 0.

## On the Basis of Variables

### One Dimensional Signals

One-dimensional signal refers to a signal that varies in only one independent variable. In the context of signals, this independent variable is typically associated with a physical dimension such as time, distance, or any other measurable quantity. One-dimensional signals are often represented as functions of a single variable.

The most common example of one-dimensional signal is a time-domain signal, where the independent variable is time. In this case, the signal’s amplitude or value changes over time, and the signal is expressed as a function of time, denoted as x(t).

### Multidimensional Signals

Multidimensional signals are used to represent data that depends on two or more independent variables. Examples of multidimensional signals include time-variable images, tomographic space-image data, and four-dimensional time-dependent space image data.

In the context of video, a typical video played on a laptop is considered a four-dimensional signal, denoted as x[k,t,r,c], where k represents the frame, t represents time, r represents the row, and c represents the column.

Other examples of multidimensional signals include static grayscale plane images, which are described by the brightness or reflectivity function of two space coordinates, f(x, y).

## On the Basis of Nature

### Periodic Signal

Periodic signal is a type of signal that repeats its pattern or waveform at regular intervals over time. The interval of repetition is called the period, denoted by T. In mathematical terms, a signal x(t) is periodic if, for all time t, the following relationship holds:

x(t+T)=x(t)

This means that the signal’s value at any given time t is the same as its value at t+T, and this pattern continues indefinitely. The period T is the smallest positive value for which this equality holds.

### Examples of Periodic Signals

Sinusoidal Waves: Pure sine waves are periodic signals with a well-defined frequency and period. The sine function repeats its values over regular intervals.

Square Waves: Square waves are periodic signals characterized by alternating high and low values, forming a square-like waveform.

Sawtooth Waves: Sawtooth waves exhibit a linear rise and a sudden drop, repeating periodically.

Periodic Pulses: Signals composed of periodic pulses, such as a train of rectangular pulses, can also be periodic.

### Aperiodic Signal

Aperiodic signal is a type of signal that does not exhibit any regular or repeating pattern over time. Unlike periodic signals, which repeat their waveforms at regular intervals, aperiodic signals lack this regularity. As a result, they do not have a well-defined period, and their waveform can be unique or irregular.

Mathematically, a signal x(t) is considered aperiodic if it does not satisfy the condition for periodicity:

x(t+T)(euall sign)x(t) for any value of T other than T=0. In other words, there is no fixed period T for which the signal’s values repeat exactly.

## On the Basis of Behaviour

### Deterministic Signals

Deterministic signals are those whose values can be modelled and evaluated using certain fixed mathematical equations or functions. They are modelled by explicit mathematical expressions, and there is no uncertainty with respect to their value at any instant of time. Deterministic signals can be used to represent situations where there is no randomness or uncertainty involved in the signal’s behavior.

### Examples of Deterministic Signals

Linear Functions: Linear functions, such as y=mx+b, where m is the slope and b is the y-intercept, are examples of deterministic signals. The value of the function at any given input can be precisely determined using the function’s formula.

Polynomial Functions: Polynomial functions, such as =anxn+an−1xn−1+⋯+a0, are also examples of deterministic signals. The coefficients an,an−1,…,a0 determine the value of the function at any given input.

Trigonometric Functions: Trigonometric functions, such as y=sin(x) or y=cos(x), are examples of deterministic signals. The values of these functions can be precisely determined using the trigonometric functions’ definitions.

### Random Signals

Random signals are also called the stochastic signals or noise; they are exhibited an element of randomness or uncertainty in their values. Unlike deterministic signals, where the values are precisely determined by a mathematical function, random signals have an inherent unpredictability. Random signals are characterized by statistical properties, and their behavior cannot be precisely predicted at any given instant.

### Examples of Random Signals

White Noise: White noise is a random signal that has equal intensity across all frequencies. It is often used as a model for background noise in various systems.

Gaussian Noise: Gaussian noise, also known as normal distribution or bell-shaped curve, is a common type of random signal. Many natural phenomena exhibit behavior close to Gaussian distribution.

Random Walk: A random walk is a mathematical model of a path that consists of a succession of random steps. It is often used to model processes with a degree of randomness.

Shot Noise: In electronics, shot noise is a type of random signal that occurs due to the discrete nature of electrons. It is prevalent in semiconductor devices.

## On the Basis of Symmetry

### Even Signal

An even signal is a signal that is symmetrical about the vertical axis or time origin. It satisfies the condition f(t)=f(−t) for all values of t. Some examples of continuous-time even signals include cosine waves and sine waves. Discrete-time even signals satisfy the condition f(−n)=f(n) for all integer values of n.

### Examples of Even Signal Functions

Even Powers of x: Functions like 2f(x)=x2, f(x)=x4, and so on, are even functions.

Cosine Function: The cosine function, f(x)=cos(x), is an even function. This is because cos(−x)=cos(x) for all x.

Absolute Value Function: The absolute value function, f(x)=∣x∣, is even. This is because ∣x∣=∣−x∣ for all x.

### Odd Signals

Odd signal is also known as an odd function, is a type of signal that exhibits symmetry with respect to the origin (usually the point (0,0)) on a coordinate system. In mathematical terms, a function f(t) is considered odd if it satisfies the condition: f(t)=−f(−t)

In simpler terms, for every value of t in the signal’s domain, the negation of the function at −t is equal to the function value at t. Graphically, this symmetry is reflected in the shape of the signal when plotted on a graph.

### Examples of Odd Signals

Sine Function: f(t)=sin(t) is an example of an odd signal. This is because sin(−t)=−sin(t) for all t.

Linear Function: f(t)=at (where a is a constant) is an odd signal, assuming a is not zero. This is because −at=−f(−t) for all t.

Cubic Function: f(t)=t3 is an odd signal.

## Other Types of Signals:

### Energy and Power Signals

Energy signal is a signal whose total energy is finite, while a power signal is a signal whose average power is finite. The distinction between energy and power signals is important in various signal processing and communication applications.

Energy Signal: An energy signal is said to be an energy signal if and only if its total energy E is finite, i.e., 0 < E < ∞. For an energy signal, the average power P = 0. Energy signals are often associated with nonperiodic signals and have finite energy over their entire duration.

Power Signal: A power signal is said to be a power signal if its average power P is finite, i.e., 0 < P < ∞. For a power signal, the total energy E = ∞. Power signals are often associated with periodic signals and have infinite energy but finite average power

### Causal and Non-Causal Signals

Causal Signals:

• Causal signal is a signal that is zero for all negative time, i.e., it exists only for t ≥ 0.
• Causal signals are used in causal systems, where the output at any time depends only on the values of the input signal up to and including that time and does not depend on future values of the input.
• Example of causal signal is the unit step function, which is defined as u(t) = 0 for t < 0 and u(t) = 1 for t ≥ 0.

### Non-Causal Signals:

• Non-causal signal is a signal that exists for both positive and negative time, i.e., it exists for all t.
• Non-causal signals are used in non-causal systems, where the output at any time depends on one or more future values of the input signal.
• Examples of non-causal signals include sine and cosine waves.

### Real Signals:

• Real signal is a signal whose values are real numbers. In other words, the amplitude of a real signal is a real quantity, and it does not have an imaginary component.
• Mathematically, a real signal is represented as x(t) where x(t)∈R, indicating that x(t) belongs to the set of real numbers.
• Example: The voltage across a resistor in an electrical circuit is a real signal. The values of the voltage are real numbers and do not involve imaginary components.

### Imaginary Signals:

• An imaginary signal is a signal whose values are purely imaginary numbers. In this case, the amplitude of the signal is an imaginary quantity, and there is no real component.
• Mathematically, an imaginary signal is represented as y(t) where y(t)∈I, indicating that y(t) belongs to the set of imaginary numbers.
• Example: In certain electrical circuits, the reactive component of voltage or current (associated with inductors or capacitors) might be modelled as an imaginary signal.

## Basic Operations of Signal

Basic signal operations involve manipulating signals through various mathematical operations. These operations can be performed on the dependent variable (amplitude) and the independent variable (time).

### Basic Signal Operations Performed on Dependent Variables

Amplitude Scaling: This involves scaling the amplitude of a signal by a certain factor.

Addition: It refers to the addition of the amplitudes of two or more signals at each instance.

Subtraction: It involves subtracting the amplitudes of two signals.

Multiplication: This operation entails multiplying the amplitudes of two signals at each instance.

### Basic Signal Operations Performed on the Independent Variable

Time Shifting: This operation results in a positive or negative “shift” of the signal along its time axis.

Time Scaling: It involves compressing or expanding the signal in time.

Time Reversal: This causes the original signal to flip along its y-axis.

## Applications of Signals in Real Life

Some common applications of signals in real life include:

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Telecommunications: Signal processing techniques are used in telecommunications to transmit, receive, and process signals over communication channels, including tasks such as modulation, demodulation, error correction, and signal amplification.

Audio and Video Processing: Signal processing techniques are getting to use in audio and video processing to optimize, analyse, and correct audio and video streams, like as filtering, compression, and noise reduction.

Image Processing: Signal processing is used in image processing to analyze and manipulate images, including tasks like image enhancement, image segmentation, and object recognition.

Speech Recognition: Signal processing techniques are applied in speech recognition to convert speech signals into text or other forms of data, enabling communication and information processing.

Biomedical Engineering: Signal processing techniques are also implemented into biomedical engineering to analyze and interpret signals, including the electrocardiograms, electroencephalograms, and other kinds of physiological data.

Financial Engineering: Signal processing techniques are also going to use in financial engineering for analyze and interpret financial data that are enabling the better decision-making and risk management.

Communication: Signals facilitate communication over various mediums, allowing information transfer over long distances.

Information Processing: Signals enable the processing and manipulation of data in various applications, from audio processing to image recognition.

Navigation: Signals, such as GPS signals, enable accurate navigation and location-based services.

Diagnostic Tools: Signals are used in medical area as diagnostic tools for monitoring and imaging.

Signal Degradation: Signals may degrade over long distances or due to interference, leading to loss of data quality.

Noise and Interference: External factors, such as electromagnetic interference or background noise, can disrupt signals.

Security Concerns: Signals transmitted wirelessly can be vulnerable to interception, raising concerns about privacy and security.

Complexity: Signal processing and analysis can be complex, requiring advanced technical knowledge and equipment.

Reliability Issues: Technical failures or disruptions can lead to signal

### What is a signal in electronics?

Signal is a physical quantity that varies along with time, space, or any other independent variable and conveys information.

### What is the purpose of signals in communication?

The main objectives of signals are to transmit information in several systems, including control systems, communication systems, and electronic circuits.

### How are signals classified?

Signals can be classified based on various properties, including continuity (analog or digital), time dependency (continuous-time or discrete-time), and periodicity.

### How many types of signal with examples?

In this article, we already have been shown different types of signals along with their example; you can check them.

### What is the difference between analog and digital signals?

Analog signals are continuous and vary smoothly over time, while digital signals consist of discrete values (usually 0s and 1s).

### How are signals used in communication systems?

Signals are used to transmit information over various communication channels. Modulation techniques are often employed to convert information into suitable carrier signals.

### What is the role of signals in control systems?

Signals in control systems refers the input and output variables that are getting to help the regulate and control the all behaviour of dynamic systems.

### How are signals represented mathematically?

Signals can be represented as mathematical functions of one or more variables, such as time.

### What are transients in signals?

Transients get the irregular occurrences as short-duration signals along with are often characterized by rapidly changes.

### How are signals processed in digital systems?

Signals in digital systems are processed by implementing the algorithms and digital signal processing techniques, with enabling tasks such as filtering, compression, and modulation.

## Summing Up

`Happy Learning!!`