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Digital Signal Processing
Digital Signal Processing
P. Ramesh Babu
ISBN 9789395245289
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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 treatment of the subject is very much simplified in order to have a thorough understanding of the subject.

  • Cover Page
  • Title Page
  • Copyright Page
  • Contents
  • Foreword
  • Preface to Seventh Revised Edition
  • Acknowledgements
  • Chapter 1 Discrete-Time Signals and Linear Systems
    • 1.1 Introduction
    • 1.2 Examples of Signals
      • 1.2.1 Speech Signal
      • 1.2.2 ECG Signal
      • 1.2.3 Electroencephalogram (EEG) Signal
    • 1.3 Classification of Signals
      • 1.3.1 Continuous-Time, Discrete-Time and Digital Signals
      • 1.3.2 Deterministic and Random Signals
    • 1.4 System
      • 1.4.1 Continuous-Time System
      • 1.4.2 Discrete-Time System
    • 1.5 Mathematical Model of Continuous-Time Systems
      • 1.5.1 Modeling of Mechanical and Electrical Elements
      • 1.5.2 Electrical Elements
    • 1.6 Examples of Continuous-Time System Models
      • 1.6.1 RL Circuit
      • 1.6.2 Mass - Spring - Dashpot System
    • 1.7 Examples of Discrete-Time System Models
      • 1.7.1 Population Model
      • 1.7.2 Savings Account
      • 1.7.3 Amortization
    • 1.8 Signal Processing
    • 1.9 Advantages and Limitations of Digital Signal Processing
      • 1.9.1 Advantages
      • 1.9.2 Limitations
    • 1.10 Applications of DSP
    • 1.11 Elementary Continuous-Time Signals
      • 1.11.1 Unit Step Function
      • 1.11.2 Unit Ramp Function
      • 1.11.3 Impulse Function
      • 1.11.4 Sinusoidal Signal
      • 1.11.5 Real Exponential Signals
      • 1.11.6 Complex Exponential Signal
    • 1.12 Continuous-Time Periodic Signals
    • 1.13 Representation of Discrete-Time Signals
      • 1.13.1 Graphical Representation
      • 1.13.2 Functional Representation
      • 1.13.3 Tabular Representation
      • 1.13.4 Sequence Representation
    • 1.14 Elementary Discrete-Time Signals
      • 1.14.1 Unit Step Sequence
      • 1.14.2 Unit Ramp Sequence
      • 1.14.3 Unit-Sample Sequence (Unit Impulse Sequence)
      • 1.14.4 Exponential Sequence
      • 1.14.5 Sinusoidal Signal
      • 1.14.6 Complex Exponential Signal
    • 1.15 Classification of Discrete-Time Signals
      • 1.15.1 Energy Signals and Power Signals
      • 1.15.2 Periodic and Aperiodic Signals
      • 1.15.3 Symmetric (Even) and Antisymmetric (Odd) Signals
      • 1.15.4 Causal and Noncausal Signals
    • 1.16 Operation on Signals
      • 1.16.1 Shifting
      • 1.16.2 Time Reversal
      • 1.16.3 Time Scaling
      • 1.16.4 Scalar Multiplication
      • 1.16.5 Signal Multiplier
      • 1.16.6 Addition Operation
    • 1.17 Sampling and Aliasing
    • 1.18 Discrete-Time System
    • 1.19 Classification of Discrete-Time Systems
      • 1.19.1 Static and Dynamic Systems
      • 1.19.2 Causal and Noncausal Systems
      • 1.19.3 Linear and Non-linear Systems
      • 1.19.4 Time Variant and Time-invariant Systems
    • 1.20 Representation of an Arbitrary Sequence
    • 1.21 Impulse Response and Convolution Sum
    • 1.22 Properties of Convolution
    • 1.23 Causality
    • 1.24 FIR and IIR Systems
    • 1.25 Stable and Unstable Systems
    • 1.26 Interconnection of LTI Systems
      • 1.26.1 Parallel Connection of Systems
      • 1.26.2 Cascade Connection of Two Systems
    • 1.27 Correlation of Two Sequences
      • 1.27.1 Cross-correlation
      • 1.27.2 Autocorrelation
      • 1.27.3 Properties of Crosscorrelation and Autocorrelation Sequences
      • 1.27.4 Computation of Correlation
      • 1.27.5 Correlation of Power and Periodic Signals
    • 1.28 Inverse System and Deconvolution
      • 1.28.1 Inverse System
      • 1.28.2 Deconvolution
    • 1.29 Time Response Analysis of Discrete-Time Systems
      • 1.29.1 Natural Response (Zero Input Response)
      • 1.29.2 Forced Response (Zero State Response)
      • 1.29.3 Total Response
    • 1.30 Impulse Response
    • 1.31 Step Response
    • 1.32 Frequency Analysis of Discrete-Time Signals
    • 1.33 Discrete Frequency Spectrum and Frequency Range
    • 1.34 Discrete-Time Fourier Transform
      • 1.34.1 Existence of Discrete-Time Fourier Transform
      • 1.34.2 Properties of Discrete-Time Fourier Transform
    • 1.35 Frequency Response Analysis of Discrete-Time Systems
      • 1.35.1 Frequency Response of First-Order System
      • 1.35.2 Frequency Response of Second-Order System
      • 1.35.3 Transfer Function
    • 1.36 Steady State and Transient Response
    • 1.37 Phase and Group Delays
    • 1.38 Ideal Filters
    • 1.39 Zero Phase and Linear Phase Transfer Functions
    • 1.40 Analog to Digital Conversion
      • 1.40.1 Sampling
      • 1.40.2 Aliasing Effect
      • 1.40.3 Sampling Theorem
      • 1.40.4 Anti-Aliasing Filter
      • 1.40.5 Sample-and-Hold Circuit
      • 1.40.6 Quantization
    • 1.41 Reconstruction of Analog Signal
    • 1.42 Sampling of Bandpass Signals
    • Questions and Answers
    • Review Questions
    • Multiple Choice Questions
    • Exercise
    • MATLAB Programs
  • Chapter 2 The Z-Transform
    • 2.1 Introduction
    • 2.2 Definition of the z-Transform
    • 2.3 z-Transform and ROC of Finite Duration Sequences
      • 2.3.1 Right-hand Sequence
      • 2.3.2 Left-hand Sequence
      • 2.3.3 Two-sided Sequence
    • 2.4 z-Transform and ROC of Infinite Duration Sequence
    • 2.5 ROC of Two-sided Sequence
    • 2.6 Stability and ROC
    • 2.7 Properties of Region of Convergence
    • 2.8 Properties of the z-Transform
    • 2.9 The System Function
    • 2.10 Poles and Zeros of a System Function
    • 2.11 Stability Criterion
    • 2.12 Relationship between the Fourier Transform and the z-Transform
    • 2.13 Relationship between s-Plane and z-Plane
    • 2.14 Inverse z-Transform
      • 2.14.1 Long Division Method
      • 2.14.2 Partial Fraction Expansion Method
      • 2.14.3 Residue Method
      • 2.14.4 Convolution Method
    • 2.15 Solution of difference Equations using One Sided z-Transform
    • 2.16 Deconvolution Using z-Transform
    • 2.17 Simple Digital Filters
      • 2.17.1 Simple IIR Digital Filters
      • 2.17.2 Highpass IIR Digital Filter
    • 2.18 Simple FIR Digital Filters
      • 2.18.1 Lowpass FIR Digital Filters
      • 2.18.2 Highpass FIR Digital Filter
    • 2.19 Comb Filter
    • 2.20 Allpass Filter
    • 2.21 Minimum Phase, Maximum Phase and Non-minimum Phase Systems
    • Questions and Answers
    • Review Questions
    • Multiple Choice Questions
    • Exercise
    • MATLAB Programs
  • Chapter 3 The Discrete Fourier Transform
    • 3.1 Introduction
    • 3.2 Discrete Fourier Series
    • 3.3 Properties of the Discrete Fourier Series
      • 3.3.1 Linearity
      • 3.3.2 Time Shifting
      • 3.3.3 Symmetry Property
      • 3.3.4 Periodic Convolution
    • 3.4 The Discrete Fourier Transform
      • 3.4.1 Time-Domain Aliasing due to Frequency Sampling
    • 3.5 Relationship of the DFT to Other Transforms
      • 3.5.1 Relationship to the Fourier Transform
      • 3.5.2 Relationship to the z-Transform
    • 3.6 Properties of the Discrete Fourier Transform
      • 3.6.1 Periodicity
      • 3.6.2 Linearity
      • 3.6.3 Circular Shift of a Sequence
      • 3.6.4 Time Reversal of the Sequence
      • 3.6.5 Circular Frequency Shift
      • 3.6.6 Complex Conjugate Property
      • 3.6.7 Circular Convolution
      • 3.6.8 Circular Correlation
      • 3.6.9 Multiplication of Two Sequences
      • 3.6.10 Parseval’s Theorem
    • 3.7 Comparison between Circular Convolution and Linear Convolution
    • 3.8 Methods to Evaluate Circular Convolution of Two Sequences
      • 3.8.1 Concentric Circle Method
      • 3.8.2 Matrix Multiplication Method
    • 3.9 Linear Convolution from Circular Convolution
    • 3.10 Filtering Long Duration Sequences
      • 3.10.1 Overlap-Save Method
      • 3.10.2 Overlap-Add Method
    • 3.11 Parameter Selection to Calculate DFT
    • Questions and Answers
    • Review Questions
    • Multiple Choice Questions
    • Exercise
    • MATLAB Programs
  • Chapter 4 The Fast Fourier Transform
    • 4.1 Introduction
    • 4.2 Direct Evaluation of the DFT
    • 4.3 The Fast Fourier Transform
    • 4.4 Decimation-in-Time Algorithm
    • 4.5 Summary of Steps of Radix - 2 DIT-FFT Algorithm
    • 4.6 Decimation-in-Frequency Algorithm
    • 4.7 Summary of Steps for Radix - 2 DIF-FFT Algorithm
    • 4.8 Differences and Similarities between DIT and DIF Algorithms
    • 4.9 IDFT using FFT Algorithm
    • 4.10 Fortran Programs for FFT
    • Questions and Answers
    • Review Questions
    • Multiple Choice Questions
    • Exercise
    • MATLAB Programs
  • Chapter 5 Infinite Impulse Response Filters
    • 5.1 Introduction
    • 5.2 Frequency Selective Filters
    • 5.3 Design of Digital Filters from Analog Filters
      • 5.3.1 Digital Versus Analog Filters
      • 5.3.2 Advantages and Disadvantages of Digital Filters
    • 5.4 Analog Lowpass Filter Design
    • 5.5 Analog Lowpass Butterworth Filter
    • 5.6 Steps to Design an Analog Butterworth Lowpass Filter
    • 5.7 Analog Lowpass Chebyshev Filters
      • 5.7.1 Pole Locations for Chebyshev Filter
      • 5.7.2 Chebyshev Type - 2 Filter
    • 5.8 Comparison between Butterworth Filter and Chebyshev Filter
    • 5.9 Steps to Design an Analog Chebyshev Lowpass Filter
    • 5.10 Frequency Transformation in Analog Domain
      • 5.10.1 Lowpass to Lowpass Filter
      • 5.10.2 Lowpass to Highpass
      • 5.10.3 Lowpass to Bandpass
      • 5.10.4 Lowpass to Bandstop
    • 5.11 Design of Highpass, Bandpass and Bandstop Filters
    • 5.12 Design of IIR Filters from Analog Filters
      • 5.12.1 Approximation of Derivatives
      • 5.12.2 Design of IIR Filter using Impulse Invariance Technique
      • 5.12.3 Design of IIR Filter using Bilinear Transformation
      • 5.12.4 The Matched z-Transform
    • 5.13 Frequency Transformation in Digital Domain
      • 5.13.1 Lowpass to Lowpass
      • 5.13.2 Lowpass to Highpass
      • 5.13.3 Lowpass to Bandpass
      • 5.13.4 Lowpass to Bandstop
    • 5.14 Realization of Digital Filters
      • 5.14.1 Direct Form I Realization
      • 5.14.2 Direct Form II Realization
      • 5.14.3 Signal Flowgraph
      • 5.14.4 Transposition Theorem and Transposed Structure
      • 5.14.5 Cascade Form
      • 5.14.6 Parallel Form Structure
      • 5.14.7 Lattice Structure of IIR System
      • 5.14.8 Conversion from Lattice Structure to Direct Form
      • 5.14.9 Conversion from Direct Form to Lattice Structure
      • 5.14.10 Lattice-Ladder Structure
      • Questions and Answers
      • Review Questions
      • Exercise
      • MATLAB Programs
    • Chapter 6 Finite Impulse Response Filters
      • 6.1 Introduction
      • 6.2 Linear Phase FIR Filters
      • 6.3 Frequency Response of Linear Phase FIR Filters
      • 6.4 Location of the Zeros of Linear Phase FIR Filters
      • 6.5 The Fourier Series Method of Designing FIR Filters
      • 6.6 Design of FIR Filters using Windows
        • 6.6.1 Rectangular Window
        • 6.6.2 The Triangular or Bartlett Window
        • 6.6.3 Raised Cosine Window
        • 6.6.4 Hanning Window
        • 6.6.5 Hamming Window
        • 6.6.6 Blackman Window
        • 6.6.7 Kaiser Window
        • 6.6.8 Summary of Windows
      • 6.7 Digital Differentiator
      • 6.8 Hilbert Transformers
      • 6.9 Frequency Sampling Method of Designing FIR Filters
        • 6.9.1 Frequency Sampling Realization
        • 6.9.2 Frequency Response
        • 6.9.3 Design
      • 6.10 Optimum Equiripple Approximation of FIR Filters
      • 6.11 Realization of FIR Filters
        • 6.11.1 Transversal Structure
        • 6.11.2 Linear Phase Realization
        • 6.11.3 Lattice Structure of an FIR Filter
        • 6.11.4 Polyphase Realization of FIR Filter
        • Questions and Answers
        • Review Questions
        • Multiple Choice Questions
        • Exercise
        • MATLAB Programs
      • Chapter 7 Finite Word Length Effects in Digital Filters
        • 7.1 Introduction
        • 7.2 Number Representation
        • 7.3 Types of Number Representation
          • 7.3.1 Fixed Point Representation
          • 7.3.2 Sign-Magnitude Form
          • 7.3.3 One’s-Complement Form
          • 7.3.4 Two’s-Complement Form
          • 7.3.5 Addition of Two Fixed Point Numbers
          • 7.3.6 Multiplication in Fixed Point Arithmetic
        • 7.4 Floating Point Numbers
          • 7.4.1 Comparison of Fixed Point and Floating Point Arithmetic
        • 7.5 Block Floating Point Numbers
        • 7.6 Quantization Noise
          • 7.6.1 Truncation
          • 7.6.2 Rounding
          • 7.6.3 Error Due to Truncation and Rounding
        • 7.7 Input Quantization Error
          • 7.7.1 Steady State Input Noise Power
          • 7.7.2 Steady State Output Noise Power
        • 7.8 Product Quantization Error
        • 7.9 Coefficient Quantization Error
        • 7.10 Zero-Input Limit Cycle Oscillations
          • 7.10.1 Dead Band
        • 7.11 Overflow Limit Cycle Oscillations
        • 7.12 Signal Scaling
        • 7.13 Quantization in Floating Point Realization of IIR Digital Filters
        • 7.14 Finite Word Length Effects in FIR Digital Filters
        • 7.15 Quantization Effects in the Computation of the DFT
        • 7.16 Quantization Errors in FFT Algorithms
        • Questions and Answers
        • Review Questions
        • Multiple Choice Questions
        • Exercise
      • Chapter 8 Multirate Signal Processing
        • 8.1 Introduction
        • 8.2 Down Sampling
        • 8.3 Spectrum of the Down Sampled Signal
        • 8.4 Upsampling
        • 8.5 Spectrum of the Up-Sampled Signal
        • 8.6 Anti-Imaging Filter
        • 8.7 Identities
          • 8.7.1 First Identity
          • 8.7.2 Second Identity
          • 8.7.3 Third Identity
          • 8.7.4 Fourth Identity
          • 8.7.5 Fifth Identity
          • 8.7.6 Sixth Identity
        • 8.8 Cascading Sample Rate Converters
        • 8.9 Efficient Transversal Structure for Decimator
        • 8.10 Efficient Transversal Structure for Interpolator
        • 8.11 Polyphase Structure of Decimator
        • 8.12 Polyphase Decimation using the z-Transform
        • 8.13 Polyphase Structure of Interpolator
        • 8.14 Polyphase Interpolation using the z-Transform
        • 8.15 Multistage Implementation of Sampling Rate Conversion
        • 8.16 Implementation of Narrow Band Lowpass Filter
        • 8.17 Filter Banks
          • 8.17.1 Analysis Filter Bank
          • 8.17.2 Synthesis Filter Bank
          • 8.17.3 Subband Coding Filter Bank
        • 8.18 Quadrature - Mirror Filter (QMF) Bank
          • 8.18.1 Alias Free Filter Bank
        • Questions and Answers
        • Review Questions
        • Multiple Choice Questions
        • MATLAB Programs
      • Chapter 9 Statistical Digital Signal Processing
        • 9.1 Introduction
        • 9.2 Random Processes
        • 9.3 Random Signal
        • 9.4 Random Variable
        • 9.5 Discrete-Time Random Signals
        • 9.6 Statistical Properties of Random Signal
        • 9.6.1 Mean
        • 9.6.2 Mean Square
        • 9.6.3 Variance
        • 9.6.4 Autocorrelation of Random Process
        • 9.6.5 Autocovariance of Random Process
        • 9.6.6 Crosscorrelation of Random Processes
        • 9.6.7 Crosscovariance of Random Processes
      • 9.7 Wide-Sense Stationary Random Process
      • 9.7.1 Power in a Random Signal
      • 9.7.2 Ergodic Process
    • 9.8 Power Density Spectrum
    • 9.9 The DTFT of the Crosscorrelation Sequence
    • 9.10 White Noise
    • 9.11 Response of LTI System due to Random Signals
    • 9.12 Estimation
    • 9.13 Estimation of Autocorrelation
    • 9.14 The Periodogram
      • 9.14.1 Average Value of IN(ω)
      • 9.14.2 Variance of the Periodogram
    • 9.15 The Use of DFT in Power Spectrum Estimation
    • 9.16 Performance Characteristics of Nonparametric Power Spectrum Estimators
      • 9.16.1 Periodogram
      • 9.16.2 Bartlett’s Power Spectrum Estimate
      • 9.16.3 Welch Power Spectrum Estimate
    • 9.17 Computational Requirements of Nonparametric Power Spectrum Estimates
      • 9.17.1 Bartlett’s Method
      • 9.17.2 Welch’s Method (50% Overlap)
      • 9.17.3 Blackman-Tukey Method
    • 9.18 Advantages and Disadvantages of Nonparametric Power Spectrum Estimation
    • Questions and Answers
    • Review Questions
    • MATLAB Programs
  • Chapter 10 Applications of Digital Signal Processing
    • 10.1 Introduction
    • 10.2 Speech Processing
    • 10.3 Speech Analysis
    • 10.4 Speech Coding
    • 10.5 Subband Coding
    • 10.6 Channel Vocoder
    • 10.7 Homomorphic Vocoder
    • 10.8 Digital Processing of Audio Signals
    • 10.9 Radar Signal Processing
    • 10.10 DSP Based Measurement System
    • Review Questions
  • Chapter 11 Digital Signal Processors
    • 11.1 Overview of Digital Signal Processors
    • 11.2 Selecting Digital Signal Processors
    • 11.3 Applications of PDSPs
      • 11.3.1 Communications Systems
      • 11.3.2 Audio Signal Processing
      • 11.3.3 Control and Data Acquisition
      • 11.3.4 Biometric Information Processing
      • 11.3.5 Image/Video Processing
    • 11.4 Von Neumann Architecture
    • 11.5 Harvard Architecture
    • 11.6 VLIW Architecture
    • 11.7 Multiply Accumulate Unit (MAC)
    • 11.8 Pipelining
    • 11.9 Architecture of TMS320C50
      • 11.9.1 Bus Structure
      • 11.9.2 Central Processing Unit
      • 11.9.3 On-Chip Memory
      • 11.9.4 On-Chip Peripherals
    • 11.10 Addressing Modes
      • 11.10.1 Immediate Addressing
      • 11.10.2 Indirect Addressing
      • 11.10.3 Register Addressing
      • 11.10.4 Memory Mapped Register Addressing
      • 11.10.5 Direct Addressing Mode
      • 11.10.6 Circular Addressing Mode
    • 11.11 Instruction Set
      • 11.11.1 Summary of Instructions
      • 11.11.2 Classication of Instructions
    • 11.12 Simple Assembly Language Programs
    • 11.13 Architecture of TMS320C54x
      • 11.13.1 Internal Memory Organization
      • 11.13.2 Overflow Handling
      • 11.13.3 The Carry Bit
      • 11.13.4 Dual 16-Bit Mode
    • 11.14 Accumulators
    • Questions and Answers
    • Review Questions
  • Appendix A Mathematical Identities
  • Appendix B Laplace Transform
  • Appendix C Answers to Selected Problems
  • Appendix D Answers to Multiple Choice Questions
  • 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.
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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 treatment of the subject is very much simplified in order to have a thorough understanding of the subject.

Table of contents
  • Cover Page
  • Title Page
  • Copyright Page
  • Contents
  • Foreword
  • Preface to Seventh Revised Edition
  • Acknowledgements
  • Chapter 1 Discrete-Time Signals and Linear Systems
    • 1.1 Introduction
    • 1.2 Examples of Signals
      • 1.2.1 Speech Signal
      • 1.2.2 ECG Signal
      • 1.2.3 Electroencephalogram (EEG) Signal
    • 1.3 Classification of Signals
      • 1.3.1 Continuous-Time, Discrete-Time and Digital Signals
      • 1.3.2 Deterministic and Random Signals
    • 1.4 System
      • 1.4.1 Continuous-Time System
      • 1.4.2 Discrete-Time System
    • 1.5 Mathematical Model of Continuous-Time Systems
      • 1.5.1 Modeling of Mechanical and Electrical Elements
      • 1.5.2 Electrical Elements
    • 1.6 Examples of Continuous-Time System Models
      • 1.6.1 RL Circuit
      • 1.6.2 Mass - Spring - Dashpot System
    • 1.7 Examples of Discrete-Time System Models
      • 1.7.1 Population Model
      • 1.7.2 Savings Account
      • 1.7.3 Amortization
    • 1.8 Signal Processing
    • 1.9 Advantages and Limitations of Digital Signal Processing
      • 1.9.1 Advantages
      • 1.9.2 Limitations
    • 1.10 Applications of DSP
    • 1.11 Elementary Continuous-Time Signals
      • 1.11.1 Unit Step Function
      • 1.11.2 Unit Ramp Function
      • 1.11.3 Impulse Function
      • 1.11.4 Sinusoidal Signal
      • 1.11.5 Real Exponential Signals
      • 1.11.6 Complex Exponential Signal
    • 1.12 Continuous-Time Periodic Signals
    • 1.13 Representation of Discrete-Time Signals
      • 1.13.1 Graphical Representation
      • 1.13.2 Functional Representation
      • 1.13.3 Tabular Representation
      • 1.13.4 Sequence Representation
    • 1.14 Elementary Discrete-Time Signals
      • 1.14.1 Unit Step Sequence
      • 1.14.2 Unit Ramp Sequence
      • 1.14.3 Unit-Sample Sequence (Unit Impulse Sequence)
      • 1.14.4 Exponential Sequence
      • 1.14.5 Sinusoidal Signal
      • 1.14.6 Complex Exponential Signal
    • 1.15 Classification of Discrete-Time Signals
      • 1.15.1 Energy Signals and Power Signals
      • 1.15.2 Periodic and Aperiodic Signals
      • 1.15.3 Symmetric (Even) and Antisymmetric (Odd) Signals
      • 1.15.4 Causal and Noncausal Signals
    • 1.16 Operation on Signals
      • 1.16.1 Shifting
      • 1.16.2 Time Reversal
      • 1.16.3 Time Scaling
      • 1.16.4 Scalar Multiplication
      • 1.16.5 Signal Multiplier
      • 1.16.6 Addition Operation
    • 1.17 Sampling and Aliasing
    • 1.18 Discrete-Time System
    • 1.19 Classification of Discrete-Time Systems
      • 1.19.1 Static and Dynamic Systems
      • 1.19.2 Causal and Noncausal Systems
      • 1.19.3 Linear and Non-linear Systems
      • 1.19.4 Time Variant and Time-invariant Systems
    • 1.20 Representation of an Arbitrary Sequence
    • 1.21 Impulse Response and Convolution Sum
    • 1.22 Properties of Convolution
    • 1.23 Causality
    • 1.24 FIR and IIR Systems
    • 1.25 Stable and Unstable Systems
    • 1.26 Interconnection of LTI Systems
      • 1.26.1 Parallel Connection of Systems
      • 1.26.2 Cascade Connection of Two Systems
    • 1.27 Correlation of Two Sequences
      • 1.27.1 Cross-correlation
      • 1.27.2 Autocorrelation
      • 1.27.3 Properties of Crosscorrelation and Autocorrelation Sequences
      • 1.27.4 Computation of Correlation
      • 1.27.5 Correlation of Power and Periodic Signals
    • 1.28 Inverse System and Deconvolution
      • 1.28.1 Inverse System
      • 1.28.2 Deconvolution
    • 1.29 Time Response Analysis of Discrete-Time Systems
      • 1.29.1 Natural Response (Zero Input Response)
      • 1.29.2 Forced Response (Zero State Response)
      • 1.29.3 Total Response
    • 1.30 Impulse Response
    • 1.31 Step Response
    • 1.32 Frequency Analysis of Discrete-Time Signals
    • 1.33 Discrete Frequency Spectrum and Frequency Range
    • 1.34 Discrete-Time Fourier Transform
      • 1.34.1 Existence of Discrete-Time Fourier Transform
      • 1.34.2 Properties of Discrete-Time Fourier Transform
    • 1.35 Frequency Response Analysis of Discrete-Time Systems
      • 1.35.1 Frequency Response of First-Order System
      • 1.35.2 Frequency Response of Second-Order System
      • 1.35.3 Transfer Function
    • 1.36 Steady State and Transient Response
    • 1.37 Phase and Group Delays
    • 1.38 Ideal Filters
    • 1.39 Zero Phase and Linear Phase Transfer Functions
    • 1.40 Analog to Digital Conversion
      • 1.40.1 Sampling
      • 1.40.2 Aliasing Effect
      • 1.40.3 Sampling Theorem
      • 1.40.4 Anti-Aliasing Filter
      • 1.40.5 Sample-and-Hold Circuit
      • 1.40.6 Quantization
    • 1.41 Reconstruction of Analog Signal
    • 1.42 Sampling of Bandpass Signals
    • Questions and Answers
    • Review Questions
    • Multiple Choice Questions
    • Exercise
    • MATLAB Programs
  • Chapter 2 The Z-Transform
    • 2.1 Introduction
    • 2.2 Definition of the z-Transform
    • 2.3 z-Transform and ROC of Finite Duration Sequences
      • 2.3.1 Right-hand Sequence
      • 2.3.2 Left-hand Sequence
      • 2.3.3 Two-sided Sequence
    • 2.4 z-Transform and ROC of Infinite Duration Sequence
    • 2.5 ROC of Two-sided Sequence
    • 2.6 Stability and ROC
    • 2.7 Properties of Region of Convergence
    • 2.8 Properties of the z-Transform
    • 2.9 The System Function
    • 2.10 Poles and Zeros of a System Function
    • 2.11 Stability Criterion
    • 2.12 Relationship between the Fourier Transform and the z-Transform
    • 2.13 Relationship between s-Plane and z-Plane
    • 2.14 Inverse z-Transform
      • 2.14.1 Long Division Method
      • 2.14.2 Partial Fraction Expansion Method
      • 2.14.3 Residue Method
      • 2.14.4 Convolution Method
    • 2.15 Solution of difference Equations using One Sided z-Transform
    • 2.16 Deconvolution Using z-Transform
    • 2.17 Simple Digital Filters
      • 2.17.1 Simple IIR Digital Filters
      • 2.17.2 Highpass IIR Digital Filter
    • 2.18 Simple FIR Digital Filters
      • 2.18.1 Lowpass FIR Digital Filters
      • 2.18.2 Highpass FIR Digital Filter
    • 2.19 Comb Filter
    • 2.20 Allpass Filter
    • 2.21 Minimum Phase, Maximum Phase and Non-minimum Phase Systems
    • Questions and Answers
    • Review Questions
    • Multiple Choice Questions
    • Exercise
    • MATLAB Programs
  • Chapter 3 The Discrete Fourier Transform
    • 3.1 Introduction
    • 3.2 Discrete Fourier Series
    • 3.3 Properties of the Discrete Fourier Series
      • 3.3.1 Linearity
      • 3.3.2 Time Shifting
      • 3.3.3 Symmetry Property
      • 3.3.4 Periodic Convolution
    • 3.4 The Discrete Fourier Transform
      • 3.4.1 Time-Domain Aliasing due to Frequency Sampling
    • 3.5 Relationship of the DFT to Other Transforms
      • 3.5.1 Relationship to the Fourier Transform
      • 3.5.2 Relationship to the z-Transform
    • 3.6 Properties of the Discrete Fourier Transform
      • 3.6.1 Periodicity
      • 3.6.2 Linearity
      • 3.6.3 Circular Shift of a Sequence
      • 3.6.4 Time Reversal of the Sequence
      • 3.6.5 Circular Frequency Shift
      • 3.6.6 Complex Conjugate Property
      • 3.6.7 Circular Convolution
      • 3.6.8 Circular Correlation
      • 3.6.9 Multiplication of Two Sequences
      • 3.6.10 Parseval’s Theorem
    • 3.7 Comparison between Circular Convolution and Linear Convolution
    • 3.8 Methods to Evaluate Circular Convolution of Two Sequences
      • 3.8.1 Concentric Circle Method
      • 3.8.2 Matrix Multiplication Method
    • 3.9 Linear Convolution from Circular Convolution
    • 3.10 Filtering Long Duration Sequences
      • 3.10.1 Overlap-Save Method
      • 3.10.2 Overlap-Add Method
    • 3.11 Parameter Selection to Calculate DFT
    • Questions and Answers
    • Review Questions
    • Multiple Choice Questions
    • Exercise
    • MATLAB Programs
  • Chapter 4 The Fast Fourier Transform
    • 4.1 Introduction
    • 4.2 Direct Evaluation of the DFT
    • 4.3 The Fast Fourier Transform
    • 4.4 Decimation-in-Time Algorithm
    • 4.5 Summary of Steps of Radix - 2 DIT-FFT Algorithm
    • 4.6 Decimation-in-Frequency Algorithm
    • 4.7 Summary of Steps for Radix - 2 DIF-FFT Algorithm
    • 4.8 Differences and Similarities between DIT and DIF Algorithms
    • 4.9 IDFT using FFT Algorithm
    • 4.10 Fortran Programs for FFT
    • Questions and Answers
    • Review Questions
    • Multiple Choice Questions
    • Exercise
    • MATLAB Programs
  • Chapter 5 Infinite Impulse Response Filters
    • 5.1 Introduction
    • 5.2 Frequency Selective Filters
    • 5.3 Design of Digital Filters from Analog Filters
      • 5.3.1 Digital Versus Analog Filters
      • 5.3.2 Advantages and Disadvantages of Digital Filters
    • 5.4 Analog Lowpass Filter Design
    • 5.5 Analog Lowpass Butterworth Filter
    • 5.6 Steps to Design an Analog Butterworth Lowpass Filter
    • 5.7 Analog Lowpass Chebyshev Filters
      • 5.7.1 Pole Locations for Chebyshev Filter
      • 5.7.2 Chebyshev Type - 2 Filter
    • 5.8 Comparison between Butterworth Filter and Chebyshev Filter
    • 5.9 Steps to Design an Analog Chebyshev Lowpass Filter
    • 5.10 Frequency Transformation in Analog Domain
      • 5.10.1 Lowpass to Lowpass Filter
      • 5.10.2 Lowpass to Highpass
      • 5.10.3 Lowpass to Bandpass
      • 5.10.4 Lowpass to Bandstop
    • 5.11 Design of Highpass, Bandpass and Bandstop Filters
    • 5.12 Design of IIR Filters from Analog Filters
      • 5.12.1 Approximation of Derivatives
      • 5.12.2 Design of IIR Filter using Impulse Invariance Technique
      • 5.12.3 Design of IIR Filter using Bilinear Transformation
      • 5.12.4 The Matched z-Transform
    • 5.13 Frequency Transformation in Digital Domain
      • 5.13.1 Lowpass to Lowpass
      • 5.13.2 Lowpass to Highpass
      • 5.13.3 Lowpass to Bandpass
      • 5.13.4 Lowpass to Bandstop
    • 5.14 Realization of Digital Filters
      • 5.14.1 Direct Form I Realization
      • 5.14.2 Direct Form II Realization
      • 5.14.3 Signal Flowgraph
      • 5.14.4 Transposition Theorem and Transposed Structure
      • 5.14.5 Cascade Form
      • 5.14.6 Parallel Form Structure
      • 5.14.7 Lattice Structure of IIR System
      • 5.14.8 Conversion from Lattice Structure to Direct Form
      • 5.14.9 Conversion from Direct Form to Lattice Structure
      • 5.14.10 Lattice-Ladder Structure
      • Questions and Answers
      • Review Questions
      • Exercise
      • MATLAB Programs
    • Chapter 6 Finite Impulse Response Filters
      • 6.1 Introduction
      • 6.2 Linear Phase FIR Filters
      • 6.3 Frequency Response of Linear Phase FIR Filters
      • 6.4 Location of the Zeros of Linear Phase FIR Filters
      • 6.5 The Fourier Series Method of Designing FIR Filters
      • 6.6 Design of FIR Filters using Windows
        • 6.6.1 Rectangular Window
        • 6.6.2 The Triangular or Bartlett Window
        • 6.6.3 Raised Cosine Window
        • 6.6.4 Hanning Window
        • 6.6.5 Hamming Window
        • 6.6.6 Blackman Window
        • 6.6.7 Kaiser Window
        • 6.6.8 Summary of Windows
      • 6.7 Digital Differentiator
      • 6.8 Hilbert Transformers
      • 6.9 Frequency Sampling Method of Designing FIR Filters
        • 6.9.1 Frequency Sampling Realization
        • 6.9.2 Frequency Response
        • 6.9.3 Design
      • 6.10 Optimum Equiripple Approximation of FIR Filters
      • 6.11 Realization of FIR Filters
        • 6.11.1 Transversal Structure
        • 6.11.2 Linear Phase Realization
        • 6.11.3 Lattice Structure of an FIR Filter
        • 6.11.4 Polyphase Realization of FIR Filter
        • Questions and Answers
        • Review Questions
        • Multiple Choice Questions
        • Exercise
        • MATLAB Programs
      • Chapter 7 Finite Word Length Effects in Digital Filters
        • 7.1 Introduction
        • 7.2 Number Representation
        • 7.3 Types of Number Representation
          • 7.3.1 Fixed Point Representation
          • 7.3.2 Sign-Magnitude Form
          • 7.3.3 One’s-Complement Form
          • 7.3.4 Two’s-Complement Form
          • 7.3.5 Addition of Two Fixed Point Numbers
          • 7.3.6 Multiplication in Fixed Point Arithmetic
        • 7.4 Floating Point Numbers
          • 7.4.1 Comparison of Fixed Point and Floating Point Arithmetic
        • 7.5 Block Floating Point Numbers
        • 7.6 Quantization Noise
          • 7.6.1 Truncation
          • 7.6.2 Rounding
          • 7.6.3 Error Due to Truncation and Rounding
        • 7.7 Input Quantization Error
          • 7.7.1 Steady State Input Noise Power
          • 7.7.2 Steady State Output Noise Power
        • 7.8 Product Quantization Error
        • 7.9 Coefficient Quantization Error
        • 7.10 Zero-Input Limit Cycle Oscillations
          • 7.10.1 Dead Band
        • 7.11 Overflow Limit Cycle Oscillations
        • 7.12 Signal Scaling
        • 7.13 Quantization in Floating Point Realization of IIR Digital Filters
        • 7.14 Finite Word Length Effects in FIR Digital Filters
        • 7.15 Quantization Effects in the Computation of the DFT
        • 7.16 Quantization Errors in FFT Algorithms
        • Questions and Answers
        • Review Questions
        • Multiple Choice Questions
        • Exercise
      • Chapter 8 Multirate Signal Processing
        • 8.1 Introduction
        • 8.2 Down Sampling
        • 8.3 Spectrum of the Down Sampled Signal
        • 8.4 Upsampling
        • 8.5 Spectrum of the Up-Sampled Signal
        • 8.6 Anti-Imaging Filter
        • 8.7 Identities
          • 8.7.1 First Identity
          • 8.7.2 Second Identity
          • 8.7.3 Third Identity
          • 8.7.4 Fourth Identity
          • 8.7.5 Fifth Identity
          • 8.7.6 Sixth Identity
        • 8.8 Cascading Sample Rate Converters
        • 8.9 Efficient Transversal Structure for Decimator
        • 8.10 Efficient Transversal Structure for Interpolator
        • 8.11 Polyphase Structure of Decimator
        • 8.12 Polyphase Decimation using the z-Transform
        • 8.13 Polyphase Structure of Interpolator
        • 8.14 Polyphase Interpolation using the z-Transform
        • 8.15 Multistage Implementation of Sampling Rate Conversion
        • 8.16 Implementation of Narrow Band Lowpass Filter
        • 8.17 Filter Banks
          • 8.17.1 Analysis Filter Bank
          • 8.17.2 Synthesis Filter Bank
          • 8.17.3 Subband Coding Filter Bank
        • 8.18 Quadrature - Mirror Filter (QMF) Bank
          • 8.18.1 Alias Free Filter Bank
        • Questions and Answers
        • Review Questions
        • Multiple Choice Questions
        • MATLAB Programs
      • Chapter 9 Statistical Digital Signal Processing
        • 9.1 Introduction
        • 9.2 Random Processes
        • 9.3 Random Signal
        • 9.4 Random Variable
        • 9.5 Discrete-Time Random Signals
        • 9.6 Statistical Properties of Random Signal
        • 9.6.1 Mean
        • 9.6.2 Mean Square
        • 9.6.3 Variance
        • 9.6.4 Autocorrelation of Random Process
        • 9.6.5 Autocovariance of Random Process
        • 9.6.6 Crosscorrelation of Random Processes
        • 9.6.7 Crosscovariance of Random Processes
      • 9.7 Wide-Sense Stationary Random Process
      • 9.7.1 Power in a Random Signal
      • 9.7.2 Ergodic Process
    • 9.8 Power Density Spectrum
    • 9.9 The DTFT of the Crosscorrelation Sequence
    • 9.10 White Noise
    • 9.11 Response of LTI System due to Random Signals
    • 9.12 Estimation
    • 9.13 Estimation of Autocorrelation
    • 9.14 The Periodogram
      • 9.14.1 Average Value of IN(ω)
      • 9.14.2 Variance of the Periodogram
    • 9.15 The Use of DFT in Power Spectrum Estimation
    • 9.16 Performance Characteristics of Nonparametric Power Spectrum Estimators
      • 9.16.1 Periodogram
      • 9.16.2 Bartlett’s Power Spectrum Estimate
      • 9.16.3 Welch Power Spectrum Estimate
    • 9.17 Computational Requirements of Nonparametric Power Spectrum Estimates
      • 9.17.1 Bartlett’s Method
      • 9.17.2 Welch’s Method (50% Overlap)
      • 9.17.3 Blackman-Tukey Method
    • 9.18 Advantages and Disadvantages of Nonparametric Power Spectrum Estimation
    • Questions and Answers
    • Review Questions
    • MATLAB Programs
  • Chapter 10 Applications of Digital Signal Processing
    • 10.1 Introduction
    • 10.2 Speech Processing
    • 10.3 Speech Analysis
    • 10.4 Speech Coding
    • 10.5 Subband Coding
    • 10.6 Channel Vocoder
    • 10.7 Homomorphic Vocoder
    • 10.8 Digital Processing of Audio Signals
    • 10.9 Radar Signal Processing
    • 10.10 DSP Based Measurement System
    • Review Questions
  • Chapter 11 Digital Signal Processors
    • 11.1 Overview of Digital Signal Processors
    • 11.2 Selecting Digital Signal Processors
    • 11.3 Applications of PDSPs
      • 11.3.1 Communications Systems
      • 11.3.2 Audio Signal Processing
      • 11.3.3 Control and Data Acquisition
      • 11.3.4 Biometric Information Processing
      • 11.3.5 Image/Video Processing
    • 11.4 Von Neumann Architecture
    • 11.5 Harvard Architecture
    • 11.6 VLIW Architecture
    • 11.7 Multiply Accumulate Unit (MAC)
    • 11.8 Pipelining
    • 11.9 Architecture of TMS320C50
      • 11.9.1 Bus Structure
      • 11.9.2 Central Processing Unit
      • 11.9.3 On-Chip Memory
      • 11.9.4 On-Chip Peripherals
    • 11.10 Addressing Modes
      • 11.10.1 Immediate Addressing
      • 11.10.2 Indirect Addressing
      • 11.10.3 Register Addressing
      • 11.10.4 Memory Mapped Register Addressing
      • 11.10.5 Direct Addressing Mode
      • 11.10.6 Circular Addressing Mode
    • 11.11 Instruction Set
      • 11.11.1 Summary of Instructions
      • 11.11.2 Classication of Instructions
    • 11.12 Simple Assembly Language Programs
    • 11.13 Architecture of TMS320C54x
      • 11.13.1 Internal Memory Organization
      • 11.13.2 Overflow Handling
      • 11.13.3 The Carry Bit
      • 11.13.4 Dual 16-Bit Mode
    • 11.14 Accumulators
    • Questions and Answers
    • Review Questions
  • Appendix A Mathematical Identities
  • Appendix B Laplace Transform
  • Appendix C Answers to Selected Problems
  • Appendix D Answers to Multiple Choice Questions
  • 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.
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