Signals and Systems: A One Semester Modular Course
- Length: 409 pages
- Edition: 1
- Language: English
- Publisher: Morgan & Claypool
- Publication Date: 2021-07-22
- ISBN-10: 163639101X
- ISBN-13: 9781636391014
- Sales Rank: #0 (See Top 100 Books)
This book is designed for use as a textbook for a one semester Signals and Systems class. It is sufficiently user friendly to be used for self study as well. It begins with a gentle introduction to the idea of abstraction by looking at numbers–the one highly abstract concept we use all the time. It then introduces some special functions that are useful for analyzing signals and systems. It then spends some time discussing some of the properties of systems; the goal being to introduce the idea of a linear time-invariant system which is the focus of the rest of the book. Fourier series, discrete and continuous time Fourier transforms are introduced as tools for the analysis of signals. The concepts of sampling and modulation which are very much a part of everyday life are discussed as applications of the these tools. Laplace transform and Z transform are then introduced as tools to analyze systems. The notions of stability of systems and feedback are analyzed using these tools.
The book is divided into thirty bite-sized modules. Each module also links up with a video lecture through a QR code in each module. The video lectures are approximately thirty minutes long. There are a set of self study questions at the end of each module along with answers to help the reader reinforce the concepts in the module.
Preface Acknowledgments What is This Course About What Do We Plan to Cover Abstractions Complex Numbers Euler's Formula Cartesian Representation Summary Exercises Answers Functions Types of Functions Continuous and Discrete Time Functions Even and Odd Functions Summary Exercises Answers Special Functions Step Function Delta Function Discrete Time Unit Impulse Function Continuous Time Delta Function or the Dirac Delta Function Summary Exercises Answers Classification of Systems Memory Invertibility Causality Stability Summary Exercises Answers Linearity and Time Invariance Linearity Scaling Additivity Time Invariance Linear Time-Invariant (LTI) Systems Summary Exercises Answers Linearity, Time-Invariance, and the Role of the Impulse Response The Response to an Impulse for a Discrete-Time System The Response to an Impulse for Continuous Time Systems The Convolution Operation Summary Exercises Answers Properties of LTI Systems Memory in LTI Systems Invertibility of LTI Systems Causality of LTI Systems Stability for LTI Systems Summary Exercises Answers Discrete Time Convolution Summary Exercises Answers Continuous Time Convolution The Impulse Response of a Simple RC Circuit Summary Exercises Answers Fourier Series Fourier Series Expansion of a Square Wave Time Frequency Duality Summary Exercises Answers Fourier Series – Properties and Interpretation Even and Odd Functions and Their Coefficients Time Shifts are Phase Shifts The Fourier Coefficients – Meaning and Extraction The Energy in a Signal Does Not Change Based on its Representation Summary Exercises Answers The Fourier Transform Extending the Frequency View to Aperiodic Functions Summary Exercises Answers Properties of the Fourier Transform Convolution Property The Differentiation Property and the Fourier Transform of the Unit Step Function Summary Exercises Answers Some More Useful Properties of the Fourier Transform Integration Property Time and Frequency Scaling Fourier Transform of Periodic Signals A Shift in Time is a Phase Change in Frequency Summary Exercises Answers Sampling The Multiplication Property of the Fourier Transform Ideal Sampling Nonideal Sampling Summary Exercises Answers Amplitude Modulation AM Reciever AM Stations in the U.S. Summary Exercises Answers Discrete Fourier Transform Discrete Time Fourier Transform (DTFT) Properties of the DTFT Differentiation in the Frequency Domain Discrete Fourier Transform Properties of the DFT Linear and Circular Shifts Linearity Time Shift Convolution The Fast Fourier Transform Summary Exercises Answers The Laplace Transform – Introduction Summary Exercises Answers Uniqueness and Linearity of the Laplace Transform The Laplace Transform is Unique – as Long as we Include the ROC in the Transform The Laplace Transform is a Linear Transform (but Be Careful with the Region of Convergence) Summary Exercises Answers Laplace Transform – Poles and Zeros Frequency Response Summary Exercises Answers The Inverse Laplace Transform Summary Exercises Answers Properties of Laplace Transforms Convolution Property Time Shifting Shifting in the S-Domain Time Scaling Differentiation in the Time Domain Differentiation in the S-Domain Integration in the Time Domain Summary Exercises Answers Analysis of Systems with Feedback Stabilizing a System Making a System More Responsive Implementing the Inverse of a System Producing a Desired Output Summary Exercises Answers Z-Transform The Z-Transform as a Generalization of the DTFT The Z-Transform in the Context of Discrete LTI Systems Exploring the Z-Transform Through Examples Summary Exercises Answers Region of Convergence for the Z-Transform Mapping Between s- and z-Planes Summary Exercises Answers Properties of the Z-Transform Linearity Convolution Time Shifting Scaling in the z-Domain Time Reversal Differentiation in the z-Domain Summary Exercises Answers The Inverse Z-Transform Inverting by Dividing Summary Exercises Answers Filters and Difference Equations Frequency Response and Poles and Zeros Finding the Input Output Relationship Designing a Simple Discrete Time Filter Summary Exercises Answers Discrete-Time Feedback Systems Stabilizing a System Producing a Desired Output Proportional Control Discrete Time PID Controllers Summary Exercises Answers Author's Biography Blank Page
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