Digital Textbook

Signals and Systems

Name: Signals and Systems
Author: Prof. Mithun Mondal

From the mathematical description of a signal to the transforms that reveal its hidden structure — and the linear time-invariant systems that shape, filter and transmit it. A complete, chapter-by-chapter course in the analysis of continuous- and discrete-time signals and systems.

Prof. Mithun Mondal EEE Undergraduate Course Free & Open Access

8Parts

29Chapters

4Core Transforms

Welcome

One language for every signal, built one chapter at a time

This is a living, web-native edition of a classic course in Signals and Systems. Each of the 29 chapters lives on its own page — readable on any device, searchable, and free to share. The journey starts with the simple question of what a signal is and how we describe it, and ends with the state-space, stochastic and communication ideas that carry the subject into modern engineering practice.

The sequence follows the standard electrical engineering curriculum, building from the classification of signals and systems through the analysis of linear time-invariant systems by convolution, then on to the four great transforms — Fourier series, the Fourier transform, the Laplace transform and the Z-transform — the sampling theorem that bridges the continuous and discrete worlds, and finally the state-space and applied topics that put the whole framework to work. Pick any chapter below to begin, or follow the eight parts in order for a complete course.

How to use this book. Each part groups chapters by theme — first the signals themselves and the systems that act on them, then the transform methods that move a problem from the time domain to a domain where it becomes simple, then sampling, discrete analysis and the applications that tie it all together. Click a chapter card to open its dedicated page with concepts, derivations, worked examples, and figures.

Part 1

Signals — The Foundations

What Is a Signal · Classification · Elementary Signals · Operations on the Independent Variable

01Introduction to Signals and Systems 02Classification of Signals 03Elementary Signals and Singularity Functions 04Signal Operations and Transformations

Part 2

Systems and LTI Analysis

System Properties · Linearity & Time-Invariance · Convolution · Impulse Response · Difference & Differential Equations

05Classification and Properties of Systems 06Linear Time-Invariant Systems 07Convolution and the Impulse Response 08Properties of LTI Systems 09Systems Described by Differential and Difference Equations

Part 3

Fourier Series

Periodic Signals · Harmonics · Convergence & Gibbs · Spectra · Response of LTI Systems

10Fourier Series Representation of Periodic Signals 11Properties and Convergence of Fourier Series 12Frequency Spectra and System Response

Part 4

The Fourier Transform

CTFT · Properties · Frequency Response & Filtering · The Discrete-Time Fourier Transform

13The Continuous-Time Fourier Transform 14Properties of the Fourier Transform 15Frequency Response and Filtering 16The Discrete-Time Fourier Transform

Part 5

The Laplace Transform

Bilateral & Unilateral · Region of Convergence · Properties · System Analysis · Stability

17The Laplace Transform and Region of Convergence 18Properties of the Laplace Transform 19System Analysis Using the Laplace Transform

Part 6

Sampling and Reconstruction

Sampling Theorem · Nyquist Rate · Aliasing · Reconstruction · Discrete-Time Processing of CT Signals

20The Sampling Theorem 21Reconstruction and Aliasing 22Discrete-Time Processing of Continuous-Time Signals

Part 7

The Z-Transform and Discrete Analysis

Z-Transform · ROC · Properties · Discrete-Time System Analysis · DFT & FFT

23The Z-Transform and Region of Convergence 24Properties of the Z-Transform 25Analysis of Discrete-Time Systems 26The Discrete Fourier Transform and FFT

Part 8

Modern Perspectives and Applications

State-Space Representation · Communications · Random Signals · Correlation & Power Spectra

27State-Space Representation of Systems 28Signals and Systems in Communications 29Random Signals and Stochastic Processes

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Start Here

Begin with Chapter 1 — Introduction to Signals and Systems

Before any transform or convolution integral, there is a question: what is a signal, what is a system, and why is the pairing so powerful? The first chapter sets the scene — the idea of a signal as a function carrying information, a system as an operator that acts on it, and the central promise of the course: that almost every engineering problem in this book becomes simple once the signal is viewed in the right domain. Open Chapter 1 →