Title:
Signals and systems
Author:
Rao, K. Deergha, author.
ISBN:
9783319686745
Personal Author:
Physical Description:
xv, 424 pages : illustrations (some color) ; 25 cm
Contents:
Machine generated contents note: 1.Introduction -- 1.1.What is a Signal? -- 1.2.What is a System? -- 1.3.Elementary Operations on Signals -- 1.3.1.Time Shifting -- 1.3.2.Time Scaling -- 1.3.3.Time Reversal -- 1.4.Classification of Signals -- 1.4.1.Continuous-Time and Discrete-Time Signals -- 1.4.2.Analog and Digital Signals -- 1.4.3.Periodic and Aperiodic Signals -- 1.4.4.Even and Odd Signals -- 1.4.5.Causal, Noncausal, and Anticausal Signal -- 1.4.6.Energy and Power Signals -- 1.4.7.Deterministic and Random Signals -- 1.5.Basic Continuous-Time Signals -- 1.5.1.The Unit Step Function -- 1.5.2.The Unit Impulse Function -- 1.5.3.The Ramp Function -- 1.5.4.The Rectangular Pulse Function -- 1.5.5.The Signum Function -- 1.5.6.The Real Exponential Function -- 1.5.7.The Complex Exponential Function -- 1.5.8.The Sine Function -- 1.6.Generation of Continuous-Time Signals Using MATLAB -- 1.7.Typical Signal Processing Operations -- 1.7.1.Correlation -- 1.7.2.Filtering
Note continued: 1.7.3.Modulation and Demodulation -- 1.7.4.Transformation -- 1.7.5.Multiplexing and Demultiplexing -- 1.8.Some Examples of Real-World Signals and Systems -- 1.8.1.Audio Recording System -- 1.8.2.Global Positioning System -- 1.8.3.Location-Based Mobile Emergency Services System -- 1.8.4.Heart Monitoring System -- 1.8.5.Human Visual System -- 1.8.6.Magnetic Resonance Imaging -- 1.9.Problems -- 1.10.MATLAB Exercises -- Further Reading -- 2.Continuous-Time Signals and Systems -- 2.1.The Representation of Signals in Terms of Impulses -- 2.2.Continuous-Time Systems -- 2.2.1.Linear Systems -- 2.2.2.Time-Invariant System -- 2.2.3.Causal System -- 2.2.4.Stable System -- 2.2.5.Memory and Memoryless System -- 2.2.6.Invertible System -- 2.2.7.Step and Impulse Responses -- 2.3.The Convolution Integral -- 2.3.1.Some Properties of the Convolution Integral -- 2.3.2.Graphical Convolution -- 2.3.3.Computation of Convolution Integral Using MATLAB
Note continued: 2.3.4.Interconnected Systems -- 2.3.5.Periodic Convolution -- 2.4.Properties of Linear Time-Invariant Continuous-Time System -- 2.4.1.LTI Systems With and Without Memory -- 2.4.2.Causality for LTI Systems -- 2.4.3.Stability for LTI Systems -- 2.4.4.Invertible LTI System -- 2.5.Systems Described by Differential Equations -- 2.5.1.Linear Constant-Coefficient Differential Equations -- 2.5.2.The General Solution of Differential Equation -- 2.5.3.Linearity -- 2.5.4.Causality -- 2.5.5.Time-Invariance -- 2.5.6.Impulse Response -- 2.5.7.Solution of Differential Equations Using MATLAB -- 2.5.8.Determining Impulse Response and Step Response for a Linear System Described by a Differential Equation Using MATLAB -- 2.6.Block-Diagram Representations of LTI Systems Described by Differential Equations -- 2.7.Singularity Functions -- 2.8.State-Space Representation of Continuous-Time LTI Systems -- 2.8.1.State and State Variables
Note continued: 2.8.2.State-Space Representation of Single-Input Single-Output Continuous-Time LTI Systems -- 2.8.3.State-Space Representation of Multi-input Multi-output Continuous-Time LTI Systems -- 2.9.Problems -- 2.10.MATLAB Exercises -- Further Reading -- 3.Frequency Domain Analysis of Continuous-Time Signals and Systems -- 3.1.Complex Exponential Fourier Series Representation of the Continuous-Time Periodic Signals -- 3.1.1.Convergence of Fourier Series -- 3.1.2.Properties of Fourier Series -- 3.2.Trigonometric Fourier Series Representation -- 3.2.1.Symmetry Conditions in Trigonometric Fourier Series -- 3.3.The Continuous Fourier Transform for Nonperiodic Signals -- 3.3.1.Convergence of Fourier Transforms -- 3.3.2.Fourier Transforms of Some Commonly Used Continuous-Time Signals -- 3.3.3.Properties of the Continuous-Time Fourier Transform -- 3.4.The Frequency Response of Continuous-Time Systems -- 3.4.1.Distortion During Transmission
Note continued: 3.5.Some Communication Application Examples -- 3.5.1.Amplitude Modulation (AM) and Demodulation Amplitude Modulation -- 3.5.2.Single-Sideband (SSB) AM -- 3.5.3.Frequency Division Multiplexing (FDM) -- 3.6.Problems -- Further Reading -- 4.Laplace Transforms -- 4.1.The Laplace Transform -- 4.1.1.Definition of Laplace Transform -- 4.1.2.The Unilateral Laplace Transform -- 4.1.3.Existence of Laplace Transforms -- 4.1.4.Relationship Between Laplace Transform and Fourier Transform -- 4.1.5.Representation of Laplace Transform in the s-Plane -- 4.2.Properties of the Region of Convergence -- 4.3.The Inverse Laplace Transform -- 4.4.Properties of the Laplace Transform -- 4.4.1.Laplace Transform Properties of Even and Odd Functions -- 4.4.2.Differentiation Property of the Unilateral Laplace Transform -- 4.4.3.Initial Value Theorem -- 4.4.4.Final Value Theorem -- 4.5.Laplace Transforms of Elementary Functions
Note continued: 4.6.Computation of Inverse Laplace Transform Using Partial Fraction Expansion -- 4.6.1.Partial Fraction Expansion of X(s) with Simple Poles -- 4.6.2.Partial Fraction Expansion of X(s) with Multiple Poles -- 4.7.Inverse Laplace Transform by Partial Fraction Expansion Using MATLAB -- 4.8.Analysis of Continuous-Time LTI Systems Using the Laplace Transform -- 4.8.1.Transfer Function -- 4.8.2.Stability and Causality -- 4.8.3.LTI Systems Characterized by Linear Constant Coefficient Differential Equations -- 4.8.4.Solution of linear Differential Equations Using Laplace Transform -- 4.8.5.Solution of Linear Differential Equations Using Laplace Transform and MATLAB -- 4.8.6.System Function for Interconnections of LTI Systems -- 4.9.Block-Diagram Representation of System Functions in the S-Domain -- 4.10.Solution of State-Space Equations Using Laplace Transform -- 4.11.Problems -- 4.12.MATLAB Exercises -- Further Reading -- 5.Analog Filters
Note continued: 5.1.Ideal Analog Filters -- 5.2.Practical Analog Low-Pass Filter Design -- 5.2.1.Filter Specifications -- 5.2.2.Butterworth Analog Low-Pass Filter -- 5.2.3.Chebyshev Analog Low-Pass Filter -- 5.2.4.Elliptic Analog Low-Pass Filter -- 5.2.5.Bessel Filter -- 5.2.6.Comparison of Various Types of Analog Filters -- 5.2.7.Design of Analog High-Pass, Band-Pass, and Band-Stop Filters -- 5.3.Effect of Poles and Zeros on Frequency Response -- 5.3.1.Effect of Two Complex System Poles on the Frequency Response -- 5.3.2.Effect of Two Complex System Zeros on the Frequency Response -- 5.4.Design of Specialized Analog Filters by Pole-Zero Placement -- 5.4.1.Notch Filter -- 5.5.Problems -- Further Reading -- 6.Discrete-Time Signals and Systems -- 6.1.The Sampling Process of Analog Signals -- 6.1.1.Impulse-Train Sampling -- 6.1.2.Sampling with a Zero-Order Hold -- 6.1.3.Quantization and Coding -- 6.2.Classification of Discrete-Time Signals
Note continued: 6.2.1.Symmetric and Anti-symmetric Signals -- 6.2.2.Finite and Infinite Length Sequences -- 6.2.3.Right-Sided and Left-Sided Sequences -- 6.2.4.Periodic and Aperiodic Signals -- 6.2.5.Energy and Power Signals -- 6.3.Discrete-Time Systems -- 6.3.1.Classification of Discrete-Time Systems -- 6.3.2.Impulse and Step Responses -- 6.4.Linear Time-Invariant Discrete-Time Systems -- 6.4.1.Input-Output Relationship -- 6.4.2.Computation of Linear Convolution -- 6.4.3.Computation of Convolution Sum Using MATLAB -- 6.4.4.Some Properties of the Convolution Sum -- 6.4.5.Stability and Causality of LTI Systems in Terms of the Impulse Response -- 6.5.Characterization of Discrete-Time Systems -- 6.5.1.Non-Recursive Difference Equation -- 6.5.2.Recursive Difference Equation -- 6.5.3.Solution of Difference Equations -- 6.5.4.Computation of Impulse and Step Responses Using MATLAB -- 6.6.Sampling of Discrete-Time Signals -- 6.6.1.Discrete-Time Down Sampler
Note continued: 6.6.2.Discrete-Time Up-Sampler -- 6.7.State-Space Representation of Discrete-Time LTI Systems -- 6.7.1.State-Space Representation of Single-Input Single-Output Discrete-Time LTI Systems -- 6.7.2.State-Space Representation of Multi-input Multi-output Discrete-Time LTI Systems -- 6.8.Problems -- 6.9.MATLAB Exercises -- Further Reading -- 7.Frequency Domain Analysis of Discrete-Time Signals and Systems -- 7.1.The Discrete-Time Fourier Series -- 7.1.1.Periodic Convolution -- 7.2.Representation of Discrete-Time Signals and Systems in Frequency Domain -- 7.2.1.Fourier Transform of Discrete-Time Signals -- 7.2.2.Theorems on DTFT -- 7.2.3.Some Properties of the DTFT of a Complex Sequence x(n) -- 7.2.4.Some Properties of the DTFT of a Real Sequence x(n) -- 7.3.Frequency Response of Discrete-Time Systems -- 7.3.1.Frequency Response Computation Using MATLAB -- 7.4.Representation of Sampling in Frequency Domain -- 7.4.1.Sampling of Low-Pass Signals
Note continued: 7.5.Reconstruction of a Band-Limited Signal from Its Samples -- 7.6.Problems -- Further Reading -- 8.The z-Transform and Analysis of Discrete Time LTI Systems -- 8.1.Definition of the z-Transform -- 8.2.Properties of the Region of Convergence for the z-Transform -- 8.3.Properties of the z-Transform -- 8.4.z-Transforms of Some Commonly Used Sequences -- 8.5.The Inverse z-Transform -- 8.5.1.Modulation Theorem in the z-Domain -- 8.5.2.Parseval's Relation in the z-Domain -- 8.6.Methods for Computation of the Inverse z-Transform -- 8.6.1.Cauchy's Residue Theorem for Computation of the Inverse z-Transform -- 8.6.2.Computation of the Inverse z-Transform Using the Partial Fraction Expansion -- 8.6.3.Inverse z-Transform by Partial Fraction Expansion Using MATLAB -- 8.6.4.Computation of the Inverse z-Transform Using the Power Series Expansion -- 8.6.5.Inverse z-Transform via Power Series Expansion Using MATLAB
Note continued: 8.6.6.Solution of Difference Equations Using the z-Transform -- 8.7.Analysis of Discrete-Time LTI Systems in the z-Transform Domain -- 8.7.1.Transfer Function -- 8.7.2.Poles and Zeros of a Transfer Function -- 8.7.3.Frequency Response from Poles and Zeros -- 8.7.4.Stability and Causality -- 8.7.5.Minimum-Phase, Maximum-Phase, and Mixed-Phase Systems -- 8.7.6.Inverse System -- 8.7.7.All-Pass System -- 8.7.8.All-Pass and Minimum-Phase Decomposition -- 8.8.One-Sided z-Transform -- 8.8.1.Solution of Difference Equations with Initial Conditions -- 8.9.Solution of State-Space Equations Using z-Transform -- 8.10.Transformations Between Continuous-Time Systems and Discrete-Time Systems -- 8.10.1.Impulse Invariance Method -- 8.10.2.Bilinear Transformation -- 8.11.Problems -- 8.12.MATLAB Exercises -- Further Reading.
Abstract:
This textbook covers the fundamental theories of signals and systems analysis, while incorporating recent developments from integrated circuits technology into its examples. Starting with basic definitions in signal theory, the text explains the properties of continuous-time and discrete-time systems and their representation by differential equations and state space. From those tools, explanations for the processes of Fourier analysis, the Laplace transform, and the z-Transform provide new ways of experimenting with different kinds of time systems. The text also covers the separate classes of analog filters and their uses in signal processing applications. Intended for undergraduate electrical engineering students, chapter sections include exercise for review and practice for the systems concepts of each chapter. Along with exercises, the text includes MATLAB-based examples to allow readers to experiment with signals and systems code on their own. An online repository of the MATLAB code from this textbook can be found at github.com/springer-math/signals-and-systems.