Signals and Systems Tutorial

Signals and systems are the fundamental building blocks of various engineering disciplines, ranging from communication engineering to digital signal processing, control engineering, and robotics. Therefore, understanding different types of signals like audio signals, video signals, digital images, etc. and systems like computers, automation systems, microcontrollers, robots, etc. is very important.

This comprehensive tutorial provides an in-depth understanding of concepts related to signals and systems. Hence, it can be a useful resource for anyone who wants to learn about signals and systems.

What are Signals and Systems?

In electronics and communication engineering, signals and systems be a core subject that deals with the study of different types of electronic signals and systems. It provides a study of how electronic signals are produced, processed, transmitted, received, and interpreted. It also provides an analysis of how different electronic systems respond to these electronic signals.

Signals and systems serve as the backbone for various engineering domains such as communication engineering, control engineering, signal processing, computer science, automation and robotics, etc.

Types of Signal

A signal is nothing but an electrical quantity like voltage, current, or electromagnetic wave used for conveying information from one point to another.

Depending on the nature, signals are classified into the following two types −

Analog Signals

Signals that have continuous variation over time and are represented using smooth, uninterrupted waveforms are referred to as analog signals. Analog signals are also referred to as continuous-time signals. Examples of analog signals include radio waves, alternating current, speed, pressure, voice signals, etc.

Digital Signals

Those electronic signals that have discrete variation with respect to time and are represented using distinct values at certain time intervals are called digital signals. Digital signals are also known as discrete-time signals. Examples of digital signals include internet signals, signals used in microprocessors, etc.

What is a System?

In electronics, a system is defined as an interconnected arrangement of circuit components like resistors, diodes, transistors, etc. used to perform a specific task on input data or signals. Some common examples of systems include amplifiers, rectifiers, modem, signal filters, etc.

Depending on the properties, electronic systems are classified into various types as discussed below −

Linear and Non-Linear Systems − Systems whose output is proportional to the applied input is known as linear system. Systems which are not linear are known as nonlinear systems.
Time-Variant and Time-Invariant Systems − Systems whose behavior vary with time for the same applied input are termed as time-variant systems. While, systems whose behavior remains the same over time for an applied input are known as time-invariant systems.
Causal and Non-Causal Systems − Systems whose output is the function of only present and past inputs and not the future input are called causal systems. Those systems whose output depends on the future inputs as well are called non-causal systems.

Importance of Signals and Systems

In the field of electronics and communication engineering, signals and systems plays a vital role because of the following key reasons −

It allows engineers to design and develop efficient devices to work with a variety of signals.
It provides tools for analyzing systems and their behavior for different types of signals; and hence allows to optimize them.
It provides information processing capabilities like encoding, decoding, modulation, demodulation, etc. which are essential for secure and effective communication of signals.
It enables engineers to develop automation and robotic systems that can process real-world signals.
Signals and systems also provides tools for filtering and modifying electronic signals used in various signal processing applications like image processing, video editing, etc.

Applications of Signals and Systems

Signals and systems is the integral part of various engineering and technology domains. Some of the common examples of applications of signals and systems are given here −

Signals and systems is used for developing efficient and high-performance technologies.
It is employed for designing and analyzing complex systems used in control engineering, signal processing, telecommunication, etc.
Signals and systems also provides tools for predicting behavior of systems for different input signals.
It helps designing communication systems for enhanced signal transmission and reception.
It provides various tools and techniques like filtering, smoothing, etc. for signal processing and enhancement.
Signals and systems is also used for designing automation and control systems that can automatically manage and control the processes to produce desired outputs.
Signals and systems provides capabilities to enhance quality of audio, video, and image files. This enhances the multimedia experiences.
It is also used as the foundational field for emerging technologies like artificial intelligence, machine learning, IoT, etc.

What You Will Learn in Signals and Systems?

This tutorial is an introductory resource covering a wide range of topics in signals and systems which are an integral part of various engineering areas, including electrical, electronics, communication, signal processing, control engineering, etc. The following table provides an overview of all the topics covered here −

Signals and Systems Overview − In this chapter, you will understand the basic meaning of signals and systems.
Signals Basic Types − This chapter provides a basic description of different types of signals like unit step, sinusoidal, exponential, etc.
Signal Classification − In this chapter, you will understand the classification of signals based on their nature and properties.
Signals Basic Operations − This section explains some basic operations performed on signals such as addition, subtraction, shifting, scaling, etc.
Systems Classification − This chapter provides the classification of systems based on their behavior.
Signals Analysis − In this chapter, you will learn about some concepts related to signals analysis such as vector, signal, orthogonality, etc.
Fourier Series − This chapter provides an overview of Fourier series and its application in signals and systems.
Fourier Series Properties − This section defines various properties of Fourier series.
Fourier Series Types − This chapter defines two important types of Fourier series namely, trigonometric and exponential Fourier series, also the relationship between them.
Fourier Transform − In this chapter, you will learn about definition and condition for existence of Fourier transform.
Fourier Transform Properties − This chapter defines various properties of Fourier transform.
Distortion Less Transmission − This chapter elaborates the concept of distortion less transmission and its mathematical analysis.
Hilbert Transform − This chapter briefly describes the Hilbert transform of a signal and its properties.
Convolution and Correlation − This chapter explains two important concepts namely convolution and correlation of signals, along with their properties.
Signals Sampling Theorem − In this chapter, you will learn about statement and proof of sampling theorem, and aliasing effecting in sampling of signals.
Signals Sampling Techniques − This chapter explains three important sampling techniques used in signals and systems namely, impulse sampling, natural sampling, and flat top sampling.
Laplace Transform − This chapter defines Laplace Transform and Inverse Laplace Transform, and also provides a relationship between Laplace and Fourier Transform.
Laplace Transform Properties − This section provides an overview of some important properties of Laplace transform
Region of Convergence (ROC) − In this chapter, you will learn about definition and properties of ROC of Laplace transform along with ROC of some basic functions.
Z-Transform − This chapter provides an overview of concepts of Z-transform and inverse Z-transform.
Z-Transform Properties − In this chapter, you will learn about some important properties of Z-transform. This chapter also explains the ROC of Z-transform along with ROC of some basic functions.

Who Should Learn Signals and Systems?

This tutorial is primarily designed for students and all enthusiastic learners, who are willing to learn signals and systems in simple and easy steps. This tutorial will give you a deep understanding on Signals and Systems concepts.

After completing this tutorial, you will be at intermediate level of expertise from where you can take yourself to higher level of expertise.

This tutorial on Signals and Systems can be also a useful resource for any of the following readers −

Students preparing for technical exams like GATE or ESE.
College or university students studying in electrical or electronics branches.
Aspirants preparing for competitive exams where signals and systems is a part of their syllabus.

Prerequisites to Learn Signals and Systems

This tutorial is written in a beginner friendly style and no prior knowledge of the subject is a necessity. However, a basic understanding of fundamental concepts like linear algebra, calculus, differential equations, complex numbers, electric circuit theory, basic electronics, etc. will be very helpful for gaining a deeper understanding of signals and systems.

FAQs on Signals and Systems

There are some very Frequently Asked Questions (FAQs) on Signals and Systems, this section tries to answer them briefly.

The most significant difference between continuous-time signal and discrete-time signal is that a continuous-time signal is defined at every instant of time, while a discrete-time signal is defined at distinct instants of time.

In the context of signals and systems, a system is a mathematical representation of a process, having definite inputs and outputs.

Fourier transform plays an important role in signal processing, as it provides a tool for converting and analyzing signals into the frequency domain, which is easier than time-domain analysis and provides a better understanding about the spectral content.

Nyquist-Shannon Sampling theorem states that a continuous-time signal if sampled at least twice of its highest frequency, then it can be accurately represented in its discrete form. It is important because it provides an essential condition to prevent aliasing effect in sampling.

Laplace transform helps converting time-domain differential equations of linear time-invariant systems into simple algebraic equations in the frequency domain for analyzing their stability and behavior.

Aliasing is an effect in signal processing which introduces new frequency components in a reconstructed signal, that were not present in the original signal before sampling. The primary cause of aliasing is under-sampling. Aliasing can be prevented by sampling the signals at a rate at least double of the highest frequency in the signal or by using an anti-aliasing filter before sampling.

Impulse response enables us to analyze the time-domain behavior of a system and understand its stability, causality, and response characteristics.

In signals and systems, convolution is a mathematical operation that works by combining two signal functions to produce a third signal function.

In signal processing, filters are systems used to modify signals for noise reduction, signal separation, or enhancement of the signals.

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