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Signals and Systems
Signals and Systems
P. Ramesh Babu, R Anandanatarajan
ISBN 9789395245319
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Table of contents

Biographical note

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This book is designed to meet the syllabi requirements of the undergraduate courses of all circuit branches of Engineering. The contents of the book are presented in a lucid style and the simple and complex problems are worked out to strengthen the theory.

  • Cover
  • Halftitle Page
  • Title Page
  • Copyright Page
  • Dedication Page
  • Contents
  • Foreword
  • Preface
  • Chapter 1 Introduction to Signals
    • 1.1 A Signal
    • 1.2 Signal Modeling
    • 1.3 Continuous-Time, Discrete-Time and Digital Signals
      • 1.3.1 Continuous-Time Signal
      • 1.3.2 Discrete-Time Signal
    • 1.4 Elementary Continuous Time Signals
      • 1.4.1 Unit Step Function
      • 1.4.2 Unit Ramp Function
      • 1.4.3 Unit Parabolic Function
      • 1.4.4 Impulse Function
      • 1.4.5 Rectangular Pulse Function
      • 1.4.6 Triangular Pulse Function
      • 1.4.7 Signum Function
      • 1.4.8 Sinc Function
      • 1.4.9 Gaussian Function
      • 1.4.10 Sinusoidal Signal
      • 1.4.11 Real Exponential Signals
      • 1.4.12 Complex Exponential Signal
    • 1.5 Representation of Discrete-Time Signals
      • 1.5.1 Graphical Representation
      • 1.5.2 Functional Representation
      • 1.5.3 Tabular Representation
      • 1.5.4 Sequence Representation
    • 1.6 Elementary Discrete-Time Signals
      • 1.6.1 Unit Step Sequence
      • 1.6.2 Unit Ramp Sequence
      • 1.6.3 Unit-Sample Sequence (Unit Impulse Sequence)
      • 1.6.4 Exponential Sequence
      • 1.6.5 Sinusoidal Signal
      • 1.6.6 Complex Exponential Signal
    • 1.7 Basic Operations on Signals
      • 1.7.1 Time Shifting
      • 1.7.2 Time Reversal
      • 1.7.3 Amplitude Scaling
      • 1.7.4 Time Scaling
      • 1.7.5 Signal Addition
      • 1.7.6 Signal Multiplication
    • 1.8 Classification of Signals
      • 1.8.1 Continuous-Time and Discrete-Time Signals
      • 1.8.2 Deterministic and Random Signals
      • 1.8.3 Periodic and Aperiodic Signals
      • 1.8.4 Symmetric (Even) and Anti-symmetric (Odd) Signals
      • 1.8.5 Energy and Power Signals
      • 1.8.6 Causal and Non-Causal Signals
    • 1.9 Signals and Vectors
      • 1.9.1 Vector
      • 1.9.2 Vector Addition
      • 1.9.3 Scalar Multiplication
      • 1.9.4 Dot Product (Inner Product)
      • 1.9.5 Norm (Length) in Rn
      • 1.9.6 Distance
      • 1.9.7 Angle
      • 1.9.8 Projection
    • 1.10 Vector Space
      • 1.10.1 Subspace
      • 1.10.2 Linear Dependence and Independence
      • 1.10.3 Spanning a Subspace
      • 1.10.4 Basis
      • 1.10.5 Orthogonality in Vectors
      • 1.10.6 Orthonormal Vectors
      • 1.10.7 Orthogonal Subspace
      • 1.10.8 Orthogonal Bases
    • 1.11 Orthogonal Vectors Space
    • 1.12 Orthogonality in Real Signals
    • 1.13 Orthogonality in Complex Signal
    • 1.14 Orthogonal Signal Space
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 2 Introduction to Systems
    • 2.1 A System
    • 2.2 Classification of Systems
      • 2.2.1 Continuous-Time and Discrete-Time Systems
      • 2.2.2 Lumped-Parameter and Distributed-Parameter Systems
      • 2.2.3 Static and Dynamic Systems
      • 2.2.4 Causal and Non-Causal Systems
      • 2.2.5 Linear and Non-Linear Systems
      • 2.2.6 Time-Invariant and Time-Variant Systems
      • 2.2.7 Stable and Unstable Systems
    • 2.3 System Modeling
      • 2.3.1 Modeling of Mechanical and Electrical Elements
      • 2.3.2 Examples of Discrete-Time System Models
    • 2.4 Invertibility and Inverse Systems
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 3 Time Domain Analysis of Discrete-Time Systems
    • 3.1 Introduction
    • 3.2 Solution of Difference Equations
    • 3.3 Natural Response (Zero-Input Response)
    • 3.4 Forced Response (Zero State Response)
    • 3.5 Total Response
    • 3.6 Impulse Response
    • 3.7 Representation of Discrete-Time Signals in Terms of Impulses
    • 3.8 Impulse Response and Convolution Sum
    • 3.9 Properties of Convolution
      • 3.9.1 The Distributive Property
      • 3.9.2 The Associative Property
      • 3.9.3 Commutative Property
      • 3.9.4 The Shifting Property
      • 3.9.5 The Convolution with an Impulse
      • 3.9.6 Convolution with a Shifted Impulse
    • 3.10 Convolution of Two Sequences
      • 3.10.1 Matrix Convolution
    • 3.11 Causality
    • 3.12 FIR and IIR Systems
    • 3.13 Stability
    • 3.14 BIBO Stability Criterion
    • 3.15 Step Response
    • 3.16 Correlation of Two Sequences
      • 3.16.1 Cross-Correlation
      • 3.16.2 Auto-Correlation
      • 3.16.3 Properties of Cross-Correlation and Auto-Correlation Sequences
      • 3.16.4 Computation of Correlation
      • 3.16.5 Correlation of Power and Periodic Signals
    • 3.17 Inverse System and Deconvolution
      • 3.17.1 Inverse System
      • 3.17.2 Deconvolution
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 4 Time Domain Analysis of Continuous-Time Systems
    • 4.1 Introduction
    • 4.2 Solution of Differential Equations (Classical Method)
      • 4.2.1 Natural Response
      • 4.2.2 Forced Response
      • 4.2.3 Total Response
    • 4.3 Representation of a Continuous-Time Signal
    • 4.4 Convolution Integral
    • 4.5 Properties of Convolution
    • 4.6 Impulse Response of Interconnected Systems
      • 4.6.1 Systems in Parallel
      • 4.6.2 Systems in Cascade
    • 4.7 Causality
    • 4.8 Graphical Procedure to Perform Convolution
    • 4.9 Stability
    • 4.10 Step Response
    • 4.11 Correlation
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 5 Fourier Series Analysis of Continuous-Time Periodic Signals
    • 5.1 Introduction
    • 5.2 Fourier Series Representation of Periodic Signals
    • 5.3 Evaluation of Fourier Coefficients
    • 5.4 Symmetry Conditions
      • 5.4.1 Half Wave Symmetry
    • 5.5 Cosine Representation
    • 5.6 Exponential Fourier Series
    • 5.7 Existence of Fourier Series
    • 5.8 Properties of Continuous-Time Fourier Series
      • 5.8.1 Linearity
      • 5.8.2 Time Shifting
      • 5.8.3 Time Reversal
      • 5.8.4 Time Scaling
      • 5.8.5 Multiplication
      • 5.8.6 Convolution
      • 5.8.7 Conjugation
      • 5.8.8 Parseval’s Theorem
    • 5.9 Power Representation using the Fourier Series
    • 5.10 Fourier Spectrum
    • 5.11 Gibb’s Phenomenon
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 6 The Continuous-Time Fourier Transform
    • 6.1 Introduction
    • 6.2 Development of Fourier Transform
    • 6.3 Existence of Fourier Transform
    • 6.4 Fourier Transform of Some Standard Signals
      • 6.4.1 Rectangular Pulse
      • 6.4.2 Triangular Pulse
    • 6.5 Properties of Fourier Transform
      • 6.5.1 Linearity
      • 6.5.2 Time Shifting
      • 6.5.3 Time Reversal
      • 6.5.4 Frequency Shifting Property
      • 6.5.5 Time Scaling
      • 6.5.6 Differentiation in Time
      • 6.5.7 Differentiation in Frequency
      • 6.5.8 Time Integration
      • 6.5.9 Conjugation
      • 6.5.10 Fourier Transform of Complex and Real Functions
      • 6.5.11 Auto-Correlation
      • 6.5.12 Duality
      • 6.5.13 Convolution
      • 6.5.14 Multiplication Property
    • 6.6 Fourier Transform of a Periodic Signal
    • 6.7 Modulation
    • 6.8 System Analysis with Fourier Transform
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 7 Signal and System Analysis using the Laplace Transform
    • 7.1 Introduction
    • 7.2 Convergence of the Laplace Transform
    • 7.3 s - Plane
    • 7.4 The Unilateral Laplace Transform
    • 7.5 Properties of Unilateral Laplace Transform
      • 7.5.1 Linearity
      • 7.5.2 Transform of Derivatives
      • 7.5.3 Transform of the Integrals
      • 7.5.4 Scaling Property
      • 7.5.5 Time Shift
      • 7.5.6 Frequency Shift
      • 7.5.7 Differentiation in the s-Domain
      • 7.5.8 Time Convolution
      • 7.5.9 Frequency Convolution
      • 7.5.10 Initial Value Theorem
      • 7.5.11 Final Value Theorem
    • 7.6 Inversion of Unilateral Laplace Transform
      • 7.6.1 Distinct Poles
      • 7.6.2 Multiple Poles
      • 7.6.3 Complex Roots
    • 7.7 Inversion of the Bilateral Laplace Transform
    • 7.8 Solution of Differential Equations using Laplace Transform
    • 7.9 Analysis of Electrical Networks using Laplace Transform
      • 7.9.1 Initial Conditions
      • 7.9.2 Transformed Form of Elements
    • 7.10 Stability
    • 7.11 Block Diagram Representation
      • 7.11.1 Summer
      • 7.11.2 Gain
      • 7.11.3 Feed Back
      • 7.11.4 Integrator
      • 7.11.5 Cascade Connection of Blocks
      • 7.11.6 Parallel Connection of Blocks
    • 7.12 Signal-Flow Graph
    • 7.13 System Realization
      • 7.13.1 Direct Form-I
      • 7.13.2 Direct Form-II
      • 7.13.3 Cascade Form
      • 7.13.4 Parallel Form Realization
    • 7.14 State Space Analysis
      • 7.14.1 State and State Variable of a System
      • 7.14.2 Procedure for Developing State Equations for RLC Networks
      • 7.14.3 State-Space Representation from System’s Transfer Function
      • 7.14.4 Derivation of Transfer Function from State Model
      • 7.14.5 Time Domain Solution of State Equation
      • 7.14.6 Laplace Transform Solution of State Equation
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 8 Fourier Analysis of Discrete-Time Signals
    • 8.1 Introduction
    • 8.2 Discrete Frequency Spectrum and Frequency Range
      • 8.2.1 Properties of Discrete Fourier Series
    • 8.3 Discrete-Time Fourier Transform
      • 8.3.1 Existence of Discrete-Time Fourier Transform
      • 8.3.2 Properties of Discrete-Time Fourier Transform
    • 8.4 Frequency Response of Discrete-Time Systems
      • 8.4.1 Frequency Response of Second Order System
    • 8.5 Transfer Function
    • 8.6 The Discrete Fourier Transform (DFT)
      • 8.6.1 Introduction
    • 8.7 Zero Padding
    • 8.8 Properties of the DFT
      • 8.8.1 Circular Convolution of Two Sequences
    • 8.9 Fast Fourier Transform (FFT)
      • 8.9.1 Decimation-in-Time Algorithm
    • 8.10 Summary of Steps of Radix - 2 DIT-FFT Algorithm
    • 8.11 Decimation-in-Frequency Algorithm
    • 8.12 Summary of Steps for Radix - 2 DIF-FFT Algorithm
    • 8.13 Differences and Similarities between DIT and DIF Algorithms
    • 8.14 IDFT using FFT Algorithm
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 9 Sampling
    • 9.1 Introduction
    • 9.2 Analog to Digital Conversion
    • 9.3 Sampling and Aliasing
    • 9.4 Impulse Sampling
    • 9.5 Sampling Theorem
    • 9.6 Anti Aliasing Filter
    • 9.7 Pulse Sampling
    • 9.8 Flat-Top Sampling
    • 9.9 Signal Reconstruction
    • 9.10 Bandpass Signals
    • 9.11 Sampling Bandpass Signals
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 10 Signal and System Analysis using the Z-Transform
    • 10.1 Introduction
    • 10.2 The z-Transform
    • 10.3 z-Transform and ROC of Finite Duration Sequences
      • 10.3.1 Right Hand Sequence
      • 10.3.2 Left Hand Sequence
      • 10.3.3 Two Sided Sequence
    • 10.4 Properties of Region of Convergence
    • 10.5 Properties of z-Transform
      • 10.5.1 Linearity
      • 10.5.2 Time Shifting
      • 10.5.3 Multiplication by an Exponential Sequence
      • 10.5.4 Time Reversal
      • 10.5.5 Multiplication by n
      • 10.5.6 Convolution
      • 10.5.7 Time Expansion
      • 10.5.8 Conjugation
      • 10.5.9 Complex Convolution Theorem
      • 10.5.10 Parseval’s Relation
      • 10.5.11 Correlation
      • 10.5.12 Initial Value Theorem
      • 10.5.13 Final Value Theorem
    • 10.6 The Inverse z-Transform
      • 10.6.1 Long Division Method
      • 10.6.2 Partial Fraction Expansion Method
      • 10.6.3 Residue Method
      • 10.6.4 Convolution Method
    • 10.7 The System Function
    • 10.8 Relationship between z-Transform and DTFT
    • 10.9 Stability Criterion
    • 10.10 Solution of Difference Equations using z-Transform
    • 10.11 Relationship between s-plane and z-plane
    • 10.12 Block Diagram Representation
      • 10.12.1 Direct Form I Realization
      • 10.12.2 Direct Form II
      • 10.12.3 Cascade Form
      • 10.12.4 Parallel Form Realization
    • 10.13 State Variable Model for Discrete-Time Systems
    • 10.14 Deconvolution using z-Transform
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 11 Signal Transmission through Linear Systems
    • 11.1 Introduction
    • 11.2 Distortionless Transmission through a System
    • 11.3 Linear Phase Systems
    • 11.4 Ideal Filters
    • 11.5 Signal Bandwidth
    • 11.6 System Bandwidth
    • 11.7 Relationship between Bandwidth and Rise Time
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Appendix A
  • Appendix B
  • Index
  • Bibliography
Dr P Ramesh Babu holds a doctorate from Indian Institute of Technology, Madras. His areas of interests include Multivariate Data Analysis, Digital Signal Processing, Control Systems and Microprocessor-based System Design. He has over 30 years of teaching and research experience. He is currently Professor in the Department of Electronics and Instrumentation Engineering, Pondicherry Engineering College, Puducherry.Dr R Anandanatarajan holds a doctorate from Anna University, Chennai. His areas of interests are Control Theory, Process Control, Computer Control of Process and Microprocessor-based System Design. He has over 30 years of teaching and research experience. He is currently Professor, Department of Electronics and Instumentation Engineering, Pondicherry Engineering College, Puducherry.
Dr R Anandanatarajan holds a doctorate from Anna University, Chennai. His areas of Interests are Control Theory, Process Control, Computer Control of Process and Microprocessor-based System Design. He has over 30 years of teaching and research experience. He is currently Professor, Department of Electronics and Instrumentation Engineering, Pondicherry Engineering College, Puducherry. 
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Description

This book is designed to meet the syllabi requirements of the undergraduate courses of all circuit branches of Engineering. The contents of the book are presented in a lucid style and the simple and complex problems are worked out to strengthen the theory.

Table of contents
  • Cover
  • Halftitle Page
  • Title Page
  • Copyright Page
  • Dedication Page
  • Contents
  • Foreword
  • Preface
  • Chapter 1 Introduction to Signals
    • 1.1 A Signal
    • 1.2 Signal Modeling
    • 1.3 Continuous-Time, Discrete-Time and Digital Signals
      • 1.3.1 Continuous-Time Signal
      • 1.3.2 Discrete-Time Signal
    • 1.4 Elementary Continuous Time Signals
      • 1.4.1 Unit Step Function
      • 1.4.2 Unit Ramp Function
      • 1.4.3 Unit Parabolic Function
      • 1.4.4 Impulse Function
      • 1.4.5 Rectangular Pulse Function
      • 1.4.6 Triangular Pulse Function
      • 1.4.7 Signum Function
      • 1.4.8 Sinc Function
      • 1.4.9 Gaussian Function
      • 1.4.10 Sinusoidal Signal
      • 1.4.11 Real Exponential Signals
      • 1.4.12 Complex Exponential Signal
    • 1.5 Representation of Discrete-Time Signals
      • 1.5.1 Graphical Representation
      • 1.5.2 Functional Representation
      • 1.5.3 Tabular Representation
      • 1.5.4 Sequence Representation
    • 1.6 Elementary Discrete-Time Signals
      • 1.6.1 Unit Step Sequence
      • 1.6.2 Unit Ramp Sequence
      • 1.6.3 Unit-Sample Sequence (Unit Impulse Sequence)
      • 1.6.4 Exponential Sequence
      • 1.6.5 Sinusoidal Signal
      • 1.6.6 Complex Exponential Signal
    • 1.7 Basic Operations on Signals
      • 1.7.1 Time Shifting
      • 1.7.2 Time Reversal
      • 1.7.3 Amplitude Scaling
      • 1.7.4 Time Scaling
      • 1.7.5 Signal Addition
      • 1.7.6 Signal Multiplication
    • 1.8 Classification of Signals
      • 1.8.1 Continuous-Time and Discrete-Time Signals
      • 1.8.2 Deterministic and Random Signals
      • 1.8.3 Periodic and Aperiodic Signals
      • 1.8.4 Symmetric (Even) and Anti-symmetric (Odd) Signals
      • 1.8.5 Energy and Power Signals
      • 1.8.6 Causal and Non-Causal Signals
    • 1.9 Signals and Vectors
      • 1.9.1 Vector
      • 1.9.2 Vector Addition
      • 1.9.3 Scalar Multiplication
      • 1.9.4 Dot Product (Inner Product)
      • 1.9.5 Norm (Length) in Rn
      • 1.9.6 Distance
      • 1.9.7 Angle
      • 1.9.8 Projection
    • 1.10 Vector Space
      • 1.10.1 Subspace
      • 1.10.2 Linear Dependence and Independence
      • 1.10.3 Spanning a Subspace
      • 1.10.4 Basis
      • 1.10.5 Orthogonality in Vectors
      • 1.10.6 Orthonormal Vectors
      • 1.10.7 Orthogonal Subspace
      • 1.10.8 Orthogonal Bases
    • 1.11 Orthogonal Vectors Space
    • 1.12 Orthogonality in Real Signals
    • 1.13 Orthogonality in Complex Signal
    • 1.14 Orthogonal Signal Space
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 2 Introduction to Systems
    • 2.1 A System
    • 2.2 Classification of Systems
      • 2.2.1 Continuous-Time and Discrete-Time Systems
      • 2.2.2 Lumped-Parameter and Distributed-Parameter Systems
      • 2.2.3 Static and Dynamic Systems
      • 2.2.4 Causal and Non-Causal Systems
      • 2.2.5 Linear and Non-Linear Systems
      • 2.2.6 Time-Invariant and Time-Variant Systems
      • 2.2.7 Stable and Unstable Systems
    • 2.3 System Modeling
      • 2.3.1 Modeling of Mechanical and Electrical Elements
      • 2.3.2 Examples of Discrete-Time System Models
    • 2.4 Invertibility and Inverse Systems
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 3 Time Domain Analysis of Discrete-Time Systems
    • 3.1 Introduction
    • 3.2 Solution of Difference Equations
    • 3.3 Natural Response (Zero-Input Response)
    • 3.4 Forced Response (Zero State Response)
    • 3.5 Total Response
    • 3.6 Impulse Response
    • 3.7 Representation of Discrete-Time Signals in Terms of Impulses
    • 3.8 Impulse Response and Convolution Sum
    • 3.9 Properties of Convolution
      • 3.9.1 The Distributive Property
      • 3.9.2 The Associative Property
      • 3.9.3 Commutative Property
      • 3.9.4 The Shifting Property
      • 3.9.5 The Convolution with an Impulse
      • 3.9.6 Convolution with a Shifted Impulse
    • 3.10 Convolution of Two Sequences
      • 3.10.1 Matrix Convolution
    • 3.11 Causality
    • 3.12 FIR and IIR Systems
    • 3.13 Stability
    • 3.14 BIBO Stability Criterion
    • 3.15 Step Response
    • 3.16 Correlation of Two Sequences
      • 3.16.1 Cross-Correlation
      • 3.16.2 Auto-Correlation
      • 3.16.3 Properties of Cross-Correlation and Auto-Correlation Sequences
      • 3.16.4 Computation of Correlation
      • 3.16.5 Correlation of Power and Periodic Signals
    • 3.17 Inverse System and Deconvolution
      • 3.17.1 Inverse System
      • 3.17.2 Deconvolution
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 4 Time Domain Analysis of Continuous-Time Systems
    • 4.1 Introduction
    • 4.2 Solution of Differential Equations (Classical Method)
      • 4.2.1 Natural Response
      • 4.2.2 Forced Response
      • 4.2.3 Total Response
    • 4.3 Representation of a Continuous-Time Signal
    • 4.4 Convolution Integral
    • 4.5 Properties of Convolution
    • 4.6 Impulse Response of Interconnected Systems
      • 4.6.1 Systems in Parallel
      • 4.6.2 Systems in Cascade
    • 4.7 Causality
    • 4.8 Graphical Procedure to Perform Convolution
    • 4.9 Stability
    • 4.10 Step Response
    • 4.11 Correlation
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 5 Fourier Series Analysis of Continuous-Time Periodic Signals
    • 5.1 Introduction
    • 5.2 Fourier Series Representation of Periodic Signals
    • 5.3 Evaluation of Fourier Coefficients
    • 5.4 Symmetry Conditions
      • 5.4.1 Half Wave Symmetry
    • 5.5 Cosine Representation
    • 5.6 Exponential Fourier Series
    • 5.7 Existence of Fourier Series
    • 5.8 Properties of Continuous-Time Fourier Series
      • 5.8.1 Linearity
      • 5.8.2 Time Shifting
      • 5.8.3 Time Reversal
      • 5.8.4 Time Scaling
      • 5.8.5 Multiplication
      • 5.8.6 Convolution
      • 5.8.7 Conjugation
      • 5.8.8 Parseval’s Theorem
    • 5.9 Power Representation using the Fourier Series
    • 5.10 Fourier Spectrum
    • 5.11 Gibb’s Phenomenon
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 6 The Continuous-Time Fourier Transform
    • 6.1 Introduction
    • 6.2 Development of Fourier Transform
    • 6.3 Existence of Fourier Transform
    • 6.4 Fourier Transform of Some Standard Signals
      • 6.4.1 Rectangular Pulse
      • 6.4.2 Triangular Pulse
    • 6.5 Properties of Fourier Transform
      • 6.5.1 Linearity
      • 6.5.2 Time Shifting
      • 6.5.3 Time Reversal
      • 6.5.4 Frequency Shifting Property
      • 6.5.5 Time Scaling
      • 6.5.6 Differentiation in Time
      • 6.5.7 Differentiation in Frequency
      • 6.5.8 Time Integration
      • 6.5.9 Conjugation
      • 6.5.10 Fourier Transform of Complex and Real Functions
      • 6.5.11 Auto-Correlation
      • 6.5.12 Duality
      • 6.5.13 Convolution
      • 6.5.14 Multiplication Property
    • 6.6 Fourier Transform of a Periodic Signal
    • 6.7 Modulation
    • 6.8 System Analysis with Fourier Transform
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 7 Signal and System Analysis using the Laplace Transform
    • 7.1 Introduction
    • 7.2 Convergence of the Laplace Transform
    • 7.3 s - Plane
    • 7.4 The Unilateral Laplace Transform
    • 7.5 Properties of Unilateral Laplace Transform
      • 7.5.1 Linearity
      • 7.5.2 Transform of Derivatives
      • 7.5.3 Transform of the Integrals
      • 7.5.4 Scaling Property
      • 7.5.5 Time Shift
      • 7.5.6 Frequency Shift
      • 7.5.7 Differentiation in the s-Domain
      • 7.5.8 Time Convolution
      • 7.5.9 Frequency Convolution
      • 7.5.10 Initial Value Theorem
      • 7.5.11 Final Value Theorem
    • 7.6 Inversion of Unilateral Laplace Transform
      • 7.6.1 Distinct Poles
      • 7.6.2 Multiple Poles
      • 7.6.3 Complex Roots
    • 7.7 Inversion of the Bilateral Laplace Transform
    • 7.8 Solution of Differential Equations using Laplace Transform
    • 7.9 Analysis of Electrical Networks using Laplace Transform
      • 7.9.1 Initial Conditions
      • 7.9.2 Transformed Form of Elements
    • 7.10 Stability
    • 7.11 Block Diagram Representation
      • 7.11.1 Summer
      • 7.11.2 Gain
      • 7.11.3 Feed Back
      • 7.11.4 Integrator
      • 7.11.5 Cascade Connection of Blocks
      • 7.11.6 Parallel Connection of Blocks
    • 7.12 Signal-Flow Graph
    • 7.13 System Realization
      • 7.13.1 Direct Form-I
      • 7.13.2 Direct Form-II
      • 7.13.3 Cascade Form
      • 7.13.4 Parallel Form Realization
    • 7.14 State Space Analysis
      • 7.14.1 State and State Variable of a System
      • 7.14.2 Procedure for Developing State Equations for RLC Networks
      • 7.14.3 State-Space Representation from System’s Transfer Function
      • 7.14.4 Derivation of Transfer Function from State Model
      • 7.14.5 Time Domain Solution of State Equation
      • 7.14.6 Laplace Transform Solution of State Equation
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 8 Fourier Analysis of Discrete-Time Signals
    • 8.1 Introduction
    • 8.2 Discrete Frequency Spectrum and Frequency Range
      • 8.2.1 Properties of Discrete Fourier Series
    • 8.3 Discrete-Time Fourier Transform
      • 8.3.1 Existence of Discrete-Time Fourier Transform
      • 8.3.2 Properties of Discrete-Time Fourier Transform
    • 8.4 Frequency Response of Discrete-Time Systems
      • 8.4.1 Frequency Response of Second Order System
    • 8.5 Transfer Function
    • 8.6 The Discrete Fourier Transform (DFT)
      • 8.6.1 Introduction
    • 8.7 Zero Padding
    • 8.8 Properties of the DFT
      • 8.8.1 Circular Convolution of Two Sequences
    • 8.9 Fast Fourier Transform (FFT)
      • 8.9.1 Decimation-in-Time Algorithm
    • 8.10 Summary of Steps of Radix - 2 DIT-FFT Algorithm
    • 8.11 Decimation-in-Frequency Algorithm
    • 8.12 Summary of Steps for Radix - 2 DIF-FFT Algorithm
    • 8.13 Differences and Similarities between DIT and DIF Algorithms
    • 8.14 IDFT using FFT Algorithm
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 9 Sampling
    • 9.1 Introduction
    • 9.2 Analog to Digital Conversion
    • 9.3 Sampling and Aliasing
    • 9.4 Impulse Sampling
    • 9.5 Sampling Theorem
    • 9.6 Anti Aliasing Filter
    • 9.7 Pulse Sampling
    • 9.8 Flat-Top Sampling
    • 9.9 Signal Reconstruction
    • 9.10 Bandpass Signals
    • 9.11 Sampling Bandpass Signals
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 10 Signal and System Analysis using the Z-Transform
    • 10.1 Introduction
    • 10.2 The z-Transform
    • 10.3 z-Transform and ROC of Finite Duration Sequences
      • 10.3.1 Right Hand Sequence
      • 10.3.2 Left Hand Sequence
      • 10.3.3 Two Sided Sequence
    • 10.4 Properties of Region of Convergence
    • 10.5 Properties of z-Transform
      • 10.5.1 Linearity
      • 10.5.2 Time Shifting
      • 10.5.3 Multiplication by an Exponential Sequence
      • 10.5.4 Time Reversal
      • 10.5.5 Multiplication by n
      • 10.5.6 Convolution
      • 10.5.7 Time Expansion
      • 10.5.8 Conjugation
      • 10.5.9 Complex Convolution Theorem
      • 10.5.10 Parseval’s Relation
      • 10.5.11 Correlation
      • 10.5.12 Initial Value Theorem
      • 10.5.13 Final Value Theorem
    • 10.6 The Inverse z-Transform
      • 10.6.1 Long Division Method
      • 10.6.2 Partial Fraction Expansion Method
      • 10.6.3 Residue Method
      • 10.6.4 Convolution Method
    • 10.7 The System Function
    • 10.8 Relationship between z-Transform and DTFT
    • 10.9 Stability Criterion
    • 10.10 Solution of Difference Equations using z-Transform
    • 10.11 Relationship between s-plane and z-plane
    • 10.12 Block Diagram Representation
      • 10.12.1 Direct Form I Realization
      • 10.12.2 Direct Form II
      • 10.12.3 Cascade Form
      • 10.12.4 Parallel Form Realization
    • 10.13 State Variable Model for Discrete-Time Systems
    • 10.14 Deconvolution using z-Transform
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Chapter 11 Signal Transmission through Linear Systems
    • 11.1 Introduction
    • 11.2 Distortionless Transmission through a System
    • 11.3 Linear Phase Systems
    • 11.4 Ideal Filters
    • 11.5 Signal Bandwidth
    • 11.6 System Bandwidth
    • 11.7 Relationship between Bandwidth and Rise Time
    • Short Questions and Answers
    • Multiple Choice Questions
    • Answers to Multiple Choice Questions
  • Appendix A
  • Appendix B
  • Index
  • Bibliography
Biographical note
Dr P Ramesh Babu holds a doctorate from Indian Institute of Technology, Madras. His areas of interests include Multivariate Data Analysis, Digital Signal Processing, Control Systems and Microprocessor-based System Design. He has over 30 years of teaching and research experience. He is currently Professor in the Department of Electronics and Instrumentation Engineering, Pondicherry Engineering College, Puducherry.Dr R Anandanatarajan holds a doctorate from Anna University, Chennai. His areas of interests are Control Theory, Process Control, Computer Control of Process and Microprocessor-based System Design. He has over 30 years of teaching and research experience. He is currently Professor, Department of Electronics and Instumentation Engineering, Pondicherry Engineering College, Puducherry.
Dr R Anandanatarajan holds a doctorate from Anna University, Chennai. His areas of Interests are Control Theory, Process Control, Computer Control of Process and Microprocessor-based System Design. He has over 30 years of teaching and research experience. He is currently Professor, Department of Electronics and Instrumentation Engineering, Pondicherry Engineering College, Puducherry. 
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