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Signals and Systems  
Author(s): P. Ramesh Babu, R Anandanatarajan
Published by Vijay Nicole Imprints Private Limited
Publication Date:  Available in all formats
ISBN: 9789395245319

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Description

Table of contents

Biographical note

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.

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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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