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Digital Signal and Image Processing Using MATLAB

Book Description

This title provides the most important theoretical aspects of Image and Signal Processing (ISP) for both deterministic and random signals. The theory is supported by exercises and computer simulations relating to real applications.

More than 200 programs and functions are provided in the MATLAB® language, with useful comments and guidance, to enable numerical experiments to be carried out, thus allowing readers to develop a deeper understanding of both the theoretical and practical aspects of this subject.

Table of Contents

  1. Coverpage
  2. Titlepage
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. Notations and Abbreviations
  8. Introduction to MATLAB
    1. 1 Variables
      1. 1.1 Vectors and matrices
      2. 1.2 Arrays
      3. 1.3 Cells and structures
    2. 2 Operations and functions
      1. 2.1 Matrix operations
      2. 2.2 Pointwise operations
      3. 2.3 Constants and initialization
      4. 2.4 Predefined matrices
      5. 2.5 Mathematical functions
      6. 2.6 Matrix functions
      7. 2.7 Other useful functions
      8. 2.8 Logical operators on boolean variables
      9. 2.9 Program loops
    3. 3 Graphically displaying results
    4. 4 Converting numbers to character strings
    5. 5 Input/output
    6. 6 Program writing
  9. Part I Deterministic Signals
    1. Chapter 1 Signal Fundamentals
      1. 1.1 The concept of signal
        1. 1.1.1 A few signals
        2. 1.1.2 Spectral representation of signals
      2. 1.2 The Concept of system
      3. 1.3 Summary
    2. Chapter 2 Discrete Time Signals and Sampling
      1. 2.1 The sampling theorem
        1. 2.1.1 Perfect reconstruction
        2. 2.1.2 Digital-to-analog conversion
      2. 2.2 Plotting a signal as a function of time
      3. 2.3 Spectral representation
        1. 2.3.1 Discrete-time Fourier transform (DTFT)
        2. 2.3.2 Discrete Fourier transform (DFT)
      4. 2.4 Fast Fourier transform
    3. Chapter 3 Spectral Observation
      1. 3.1 Spectral accuracy and resolution
        1. 3.1.1 Observation of a complex exponential
        2. 3.1.2 Plotting accuracy of the DTFT
        3. 3.1.3 Frequency resolution
        4. 3.1.4 Effects of windowing on the resolution
      2. 3.2 Short term Fourier transform
      3. 3.3 Summing up
      4. 3.4 Application examples and exercises
        1. 3.4.1 Amplitude modulations
        2. 3.4.2 Frequency modulation
    4. Chapter 4 Linear Filters
      1. 4.1 Definitions and properties
      2. 4.2 The z-transform
        1. 4.2.1 Definition and properties
        2. 4.2.2 A few examples
      3. 4.3 Transforms and linear filtering
      4. 4.4 Difference equations and rational TF filters
        1. 4.4.1 Stability considerations
        2. 4.4.2 FIR and IIR filters
        3. 4.4.3 Causal solution and initial conditions
        4. 4.4.4 Calculating the responses
        5. 4.4.5 Stability and the Jury test
      5. 4.5 Connection between gain and poles/zeros
      6. 4.6 Minimum phase filters
      7. 4.7 Filter design methods
        1. 4.7.1 Going from the continuous-time filter to the discretetime filter
        2. 4.7.2 FIR filter design using the window method
        3. 4.7.3 IIR filter design
      8. 4.8 Oversampling and undersampling
        1. 4.8.1 Oversampling
        2. 4.8.2 Undersampling
    5. Chapter 5 Filter Implementation
      1. 5.1 Filter implementation
        1. 5.1.1 Examples of filter structures
        2. 5.1.2 Distributing the calculation load in an FIR filter
        3. 5.1.3 FIR block filtering
        4. 5.1.4 FFT filtering
      2. 5.2 Filter banks
        1. 5.2.1 Decimation and expansion
        2. 5.2.2 Filter banks
    6. Chapter 6 An Introduction to Image Processing
      1. 6.1 Introduction
        1. 6.1.1 Image display, color palette
        2. 6.1.2 Importing images
        3. 6.1.3 Arithmetical and logical operations
      2. 6.2 Geometric transformations of an image
        1. 6.2.1 The typical transformations
        2. 6.2.2 Aligning images
      3. 6.3 Frequential content of an image
      4. 6.4 Linear filtering
      5. 6.5 Other operations on images
        1. 6.5.1 Undersampling
        2. 6.5.2 Oversampling
        3. 6.5.3 Contour detection
        4. 6.5.4 Median filtering
        5. 6.5.5 Maximum enhancement
        6. 6.5.6 Image binarization
        7. 6.5.7 Morphological filtering of binary images
      6. 6.6 JPEG lossy compression
        1. 6.6.1 Basic algorithm
        2. 6.6.2 Writing the compression function
        3. 6.6.3 Writing the decompression function
      7. 6.7 Watermarking
        1. 6.7.1 Spatial image watermarking
        2. 6.7.2 Spectral image watermarking
  10. Part II Random Signals
    1. Chapter 7 Random Variables
      1. 7.1 Random phenomena in signal processing
      2. 7.2 Basic concepts of random variables
      3. 7.3 Common probability distributions
        1. 7.3.1 Uniform probability distribution on (a, b)
        2. 7.3.2 Real Gaussian random variable
        3. 7.3.3 Complex Gaussian random variable
        4. 7.3.4 Generating the common probability distributions
        5. 7.3.5 Estimating the probability density
        6. 7.3.6 Gaussian random vectors
      4. 7.4 Generating an r.v. with any type of p.d.
      5. 7.5 Uniform quantization
    2. Chapter 8 Random Processes
      1. 8.1 Introduction
      2. 8.2 Wide-sense stationary processes
        1. 8.2.1 Definitions and properties of WSS processes
        2. 8.2.2 Spectral representation of a WSS process
        3. 8.2.3 Sampling a WSS process
      3. 8.3 Estimating the covariance
      4. 8.4 Filtering formulae for WSS random processes
      5. 8.5 MA, AR and ARMA time series
        1. 8.5.1 Q order MA (Moving Average) process
        2. 8.5.2 P order AR (Autoregressive) Process
        3. 8.5.3 The Levinson algorithm
        4. 8.5.4 ARMA (P, Q) process
    3. Chapter 9 Continuous Spectra Estimation
      1. 9.1 Non-parametric estimation of the PSD
        1. 9.1.1 Estimation from the autocovariance function
        2. 9.1.2 Estimation based on the periodogram
      2. 9.2 Parametric estimation
        1. 9.2.1 AR estimation
        2. 9.2.2 Estimating the spectrum of an AR process
        3. 9.2.3 The Durbin method of MA estimation
    4. Chapter 10 Discrete Spectra Estimation
      1. 10.1 Estimating the amplitudes and the frequencies
        1. 10.1.1 The case of a single complex exponential
        2. 10.1.2 Real harmonic mixtures
        3. 10.1.3 Complex harmonic mixtures
      2. 10.2 Periodograms and the resolution limit
      3. 10.3 High resolution methods
        1. 10.3.1 Periodic signals and recursive equations
        2. 10.3.2 The Prony method
        3. 10.3.3 The MUSIC algorithm
        4. 10.3.4 Introduction to array processing
    5. Chapter 11 The Least Squares Method
      1. 11.1 The projection theorem
      2. 11.2 The least squares method
        1. 11.2.1 Formulating the problem
        2. 11.2.2 The linear model
        3. 11.2.3 The least squares estimator
        4. 11.2.4 The RLS algorithm (recursive least squares)
        5. 11.2.5 Identifying the impulse response of a channel
      3. 11.3 Linear predictions of the WSS processes
        1. 11.3.1 Yule-Walker equations
        2. 11.3.2 Predicting a WSS harmonic process
        3. 11.3.3 Predicting a causal AR-P process
        4. 11.3.4 Reflection coefficients and lattice filters
      4. 11.4 Wiener filtering
        1. 11.4.1 Finite impulse response solution
        2. 11.4.2 Gradient algorithm
        3. 11.4.3 Wiener equalization
      5. 11.5 The LMS (least mean square) algorithm
        1. 11.5.1 The constant step algorithm
        2. 11.5.2 The normalized LMS algorithm
        3. 11.5.3 Echo canceling
      6. 11.6 Application: the Kalman algorithm
        1. 11.6.1 The Kalman filter
        2. 11.6.2 The vector case
    6. Chapter 12 Selected Topics
      1. 12.1 Simulation of continuous-time systems
        1. 12.1.1 Simulation by approximation
        2. 12.1.2 Exact model simulation
      2. 12.2 Dual Tone Multi-Frequency (DTMF)
      3. 12.3 Speech processing
        1. 12.3.1 A speech signal model
        2. 12.3.2 Compressing a speech signal
      4. 12.4 DTW
      5. 12.5 Modifying the duration of an audio signal
        1. 12.5.1 PSOLA
        2. 12.5.2 Phase vocoder
      6. 12.6 Quantization noise shaping
      7. 12.7 Elimination of the background noise in audio
      8. 12.8 Eliminating the impulse noise
        1. 12.8.1 The signal model
        2. 12.8.2 Click detection
        3. 12.8.3 Restoration
      9. 12.9 Tracking the cardiac rhythm of the fetus
        1. 12.9.1 Objectives
        2. 12.9.2 Separating the EKG signals
        3. 12.9.3 Estimating cardiac rhythms
      10. 12.10 Extracting the contour of a coin
      11. 12.11 Principal component analysis (PCA)
        1. 12.11.1 Determining the principal components
        2. 12.11.2 2-Dimension PCA
        3. 12.11.3 Linear discriminant analysis (LDA)
      12. 12.12 Separating an instantaneous mixture
      13. 12.13 Matched filters in radar telemetry
      14. 12.14 Kalman filtering
      15. 12.15 Compression
        1. 12.15.1 Scalar quantization
        2. 12.15.2 Vector quantization
      16. 12.16 Digital communications
        1. 12.16.1 Introduction
        2. 12.16.2 8-phase shift keying (PSK)
        3. 12.16.3 PAM modulation
        4. 12.16.4 Spectrum of a digital signal
        5. 12.16.5 The Nyquist criterion in digital communications
        6. 12.16.6 The eye pattern
        7. 12.16.7 PAM modulation on the Nyquist channel
      17. 12.17 Linear equalization and the Viterbi algorithm
        1. 12.17.1 Linear equalization
        2. 12.17.2 The Viterbi algorithm
  11. Part III Hints and Solutions
    1. Chapter 13 Hints and Solutions
      1. H1 Signal fundamentals
      2. H2 Discrete time signals and sampling
      3. H3 Spectral observation
      4. H4 Linear filters
      5. H5 Filter implementation
      6. H6 An Introduction to image processing
      7. H7 Random variables
      8. H8 Random processes
      9. H9 Continuous spectra estimation
      10. H10 Discrete spectra estimation
      11. H11 The least squares method
      12. H12 Selected topics
    2. Chapter 14 Appendix
      1. A1 Fourier transform
      2. A2 Discrete time Fourier transform
      3. A3 Discrete Fourier transform
      4. A4 z-Transform
      5. A5 Jury criterion
      6. A6 FFT filtering algorithms revisited
  12. Bibliography
  13. Index