book

Digital Signal and Image Processing Using MATLAB

Name: Digital Signal and Image Processing Using MATLAB
ISBN: 9781905209132

by Gérard Blanchet, Maurice Charbit

May 2006

Intermediate to advanced

763 pages

16h 57m

English

Wiley

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Coverpage
Titlepage
Copyright
Dedication
Contents
Preface
Notations and Abbreviations
Introduction to MATLAB
1 Variables1.1 Vectors and matrices1.2 Arrays1.3 Cells and structures2 Operations and functions2.1 Matrix operations2.2 Pointwise operations2.3 Constants and initialization2.4 Predefined matrices2.5 Mathematical functions2.6 Matrix functions2.7 Other useful functions2.8 Logical operators on boolean variables2.9 Program loops3 Graphically displaying results4 Converting numbers to character strings5 Input/output6 Program writing
Part I Deterministic Signals
Chapter 1 Signal Fundamentals
1.1 The concept of signal1.1.1 A few signals1.1.2 Spectral representation of signals1.2 The Concept of system1.3 Summary

Chapter 2 Discrete Time Signals and Sampling
2.1 The sampling theorem2.1.1 Perfect reconstruction2.1.2 Digital-to-analog conversion2.2 Plotting a signal as a function of time2.3 Spectral representation2.3.1 Discrete-time Fourier transform (DTFT)2.3.2 Discrete Fourier transform (DFT)2.4 Fast Fourier transform
Chapter 3 Spectral Observation
3.1 Spectral accuracy and resolution3.1.1 Observation of a complex exponential3.1.2 Plotting accuracy of the DTFT3.1.3 Frequency resolution3.1.4 Effects of windowing on the resolution3.2 Short term Fourier transform3.3 Summing up3.4 Application examples and exercises3.4.1 Amplitude modulations3.4.2 Frequency modulation
Chapter 4 Linear Filters
4.1 Definitions and properties4.2 The z-transform4.2.1 Definition and properties4.2.2 A few examples4.3 Transforms and linear filtering4.4 Difference equations and rational TF filters4.4.1 Stability considerations4.4.2 FIR and IIR filters4.4.3 Causal solution and initial conditions4.4.4 Calculating the responses4.4.5 Stability and the Jury test4.5 Connection between gain and poles/zeros4.6 Minimum phase filters4.7 Filter design methods4.7.1 Going from the continuous-time filter to the discretetime filter4.7.2 FIR filter design using the window method4.7.3 IIR filter design4.8 Oversampling and undersampling4.8.1 Oversampling4.8.2 Undersampling
Chapter 5 Filter Implementation
5.1 Filter implementation5.1.1 Examples of filter structures5.1.2 Distributing the calculation load in an FIR filter5.1.3 FIR block filtering5.1.4 FFT filtering5.2 Filter banks5.2.1 Decimation and expansion5.2.2 Filter banks
Chapter 6 An Introduction to Image Processing
6.1 Introduction6.1.1 Image display, color palette6.1.2 Importing images6.1.3 Arithmetical and logical operations6.2 Geometric transformations of an image6.2.1 The typical transformations6.2.2 Aligning images6.3 Frequential content of an image6.4 Linear filtering6.5 Other operations on images6.5.1 Undersampling6.5.2 Oversampling6.5.3 Contour detection6.5.4 Median filtering6.5.5 Maximum enhancement6.5.6 Image binarization6.5.7 Morphological filtering of binary images6.6 JPEG lossy compression6.6.1 Basic algorithm6.6.2 Writing the compression function6.6.3 Writing the decompression function6.7 Watermarking6.7.1 Spatial image watermarking6.7.2 Spectral image watermarking
Part II Random Signals
Chapter 7 Random Variables
7.1 Random phenomena in signal processing7.2 Basic concepts of random variables7.3 Common probability distributions7.3.1 Uniform probability distribution on (a, b)7.3.2 Real Gaussian random variable7.3.3 Complex Gaussian random variable7.3.4 Generating the common probability distributions7.3.5 Estimating the probability density7.3.6 Gaussian random vectors7.4 Generating an r.v. with any type of p.d.7.5 Uniform quantization
Chapter 8 Random Processes
8.1 Introduction8.2 Wide-sense stationary processes8.2.1 Definitions and properties of WSS processes8.2.2 Spectral representation of a WSS process8.2.3 Sampling a WSS process8.3 Estimating the covariance8.4 Filtering formulae for WSS random processes8.5 MA, AR and ARMA time series8.5.1 Q order MA (Moving Average) process8.5.2 P order AR (Autoregressive) Process8.5.3 The Levinson algorithm8.5.4 ARMA (P, Q) process
Chapter 9 Continuous Spectra Estimation
9.1 Non-parametric estimation of the PSD9.1.1 Estimation from the autocovariance function9.1.2 Estimation based on the periodogram9.2 Parametric estimation9.2.1 AR estimation9.2.2 Estimating the spectrum of an AR process9.2.3 The Durbin method of MA estimation
Chapter 10 Discrete Spectra Estimation
10.1 Estimating the amplitudes and the frequencies10.1.1 The case of a single complex exponential10.1.2 Real harmonic mixtures10.1.3 Complex harmonic mixtures10.2 Periodograms and the resolution limit10.3 High resolution methods10.3.1 Periodic signals and recursive equations10.3.2 The Prony method10.3.3 The MUSIC algorithm10.3.4 Introduction to array processing
Chapter 11 The Least Squares Method
11.1 The projection theorem11.2 The least squares method11.2.1 Formulating the problem11.2.2 The linear model11.2.3 The least squares estimator11.2.4 The RLS algorithm (recursive least squares)11.2.5 Identifying the impulse response of a channel11.3 Linear predictions of the WSS processes11.3.1 Yule-Walker equations11.3.2 Predicting a WSS harmonic process11.3.3 Predicting a causal AR-P process11.3.4 Reflection coefficients and lattice filters11.4 Wiener filtering11.4.1 Finite impulse response solution11.4.2 Gradient algorithm11.4.3 Wiener equalization11.5 The LMS (least mean square) algorithm11.5.1 The constant step algorithm11.5.2 The normalized LMS algorithm11.5.3 Echo canceling11.6 Application: the Kalman algorithm11.6.1 The Kalman filter11.6.2 The vector case
Chapter 12 Selected Topics
12.1 Simulation of continuous-time systems12.1.1 Simulation by approximation12.1.2 Exact model simulation12.2 Dual Tone Multi-Frequency (DTMF)12.3 Speech processing12.3.1 A speech signal model12.3.2 Compressing a speech signal12.4 DTW12.5 Modifying the duration of an audio signal12.5.1 PSOLA12.5.2 Phase vocoder12.6 Quantization noise shaping12.7 Elimination of the background noise in audio12.8 Eliminating the impulse noise12.8.1 The signal model12.8.2 Click detection12.8.3 Restoration12.9 Tracking the cardiac rhythm of the fetus12.9.1 Objectives12.9.2 Separating the EKG signals12.9.3 Estimating cardiac rhythms12.10 Extracting the contour of a coin12.11 Principal component analysis (PCA)12.11.1 Determining the principal components12.11.2 2-Dimension PCA12.11.3 Linear discriminant analysis (LDA)12.12 Separating an instantaneous mixture12.13 Matched filters in radar telemetry12.14 Kalman filtering12.15 Compression12.15.1 Scalar quantization12.15.2 Vector quantization12.16 Digital communications12.16.1 Introduction12.16.2 8-phase shift keying (PSK)12.16.3 PAM modulation12.16.4 Spectrum of a digital signal12.16.5 The Nyquist criterion in digital communications12.16.6 The eye pattern12.16.7 PAM modulation on the Nyquist channel12.17 Linear equalization and the Viterbi algorithm12.17.1 Linear equalization12.17.2 The Viterbi algorithm
Part III Hints and Solutions
Chapter 13 Hints and Solutions
H1 Signal fundamentalsH2 Discrete time signals and samplingH3 Spectral observationH4 Linear filtersH5 Filter implementationH6 An Introduction to image processingH7 Random variablesH8 Random processesH9 Continuous spectra estimationH10 Discrete spectra estimationH11 The least squares methodH12 Selected topics
Chapter 14 Appendix
A1 Fourier transformA2 Discrete time Fourier transformA3 Discrete Fourier transformA4 z-TransformA5 Jury criterionA6 FFT filtering algorithms revisited
Bibliography
Index

Content preview from Digital Signal and Image Processing Using MATLAB

Chapter 13 Hints and Solutions

H1 Signal fundamentals

H2 Discrete time signals and sampling

H2.1 (An illustration of the sampling theorem) (see page 63)

Because F_s = 500 Hz is greater than twice the signal's frequency (that is, 2 × 200 Hz), the sampling makes it possible to perfectly reconstruct the signal. Hence we end up with the same sine at the 200 Hz frequency.
Because F_s = 250 Hz is smaller than twice the signal's frequency, the sampling introduces aliasing. The ±F_s shifts in the spectrum (corresponding to n = ±1 in formula 2.5) contribute to the frequency with − 250 + 200 = 50 Hz. Since the spectrum is symmetrical, everything happens as if the 200 Hz frequency were “aliased” by symmetry about the frequency F_s/2 = 125 Hz. The result of the reconstruction is a sine with the frequency 50 Hz (Figure H2.1).
Type:
%===== CECHAN2.M Ds=.1; % Signal length F0=200; % Frequency of the sine function Fs=input('Sampling frequency in Hz (F0=200 Hz) = '); Ts=1/Fs; Ne=Ds/Ts+1; % Number of samples K=40; % Interpolation fonction for displaying Tc=Ts/K; Nc=Ds/Tc+1; % Nb points of the "continuous" signal %================= tpc=[0:Nc-1]*Tc; xtc=cos(2*pi*tpc*F0); % "Continuous" signal tpe=[0:Ne-1]*Ts; xte=cos(2*pi*tpe*F0); % Samples subplot(211); plot(tpc,xtc,'-',tpe,xte,'o'); %===== Interpolation function ht=sin(pi*Fs*tpc) ./ tpc /Fs / pi; ht(1)=1; Ni=200; % Reconstruction filter hti=[ht(Ni:-1:2) ht(1:Ni)]; % (length 2*Ni-1) ...

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Digital Signal and Image Processing Using MATLAB

by Gérard Blanchet, Maurice Charbit

Chapter 13