Digital Signal and Image Processing Using MATLAB

by Blanchet, Gé; rard; Charbit, Maurice

• ISBN13: 9781905209132
• ISBN10: 1905209134
• Format: Hardcover
• Copyright: 2006-05-22
• Publisher: Iste/Hermes Science Pub

Summary

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 MATLABr 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.

Author Biography

GTrard Blanchet is the author of several books on automatic control systems, digital signal processing, and computer architecture. Maurice Charbit is a researcher in the areas of statistics, speech, and image processing. They are both professors at the +cole Nationale SupTrieure des TTlTcommunications–Paris.

Table of Contents

Preface	15	(4)
Notations and Abbreviations	19	(4)
Introduction to MATLAB	23	(1)
1 Variables	24	(5)
1.1 Vectors and matrices	24	(2)
1.2 Arrays	26	(1)
1.3 Cells and structures	27	(2)
2 Operations and functions	29	(7)
2.1 Matrix operations	29	(1)
2.2 Pointwise operations	30	(1)
2.3 Constants and initialization	31	(1)
2.4 Predefined matrices	31	(1)
2.5 Mathematical functions	32	(2)
2.6 Matrix functions	34	(1)
2.7 Other useful functions	34	(1)
2.8 Logical operators on boolean variables	35	(1)
2.9 Program loops	35	(1)
3 Graphically displaying results	36	(3)
4 Converting numbers to character strings	39	(1)
5 Input/output	39	(1)
6 Program writing	40	(1)
Part I Deterministic Signals	41	(204)
Chapter 1 Signal Fundamentals	43	(8)
1.1 The concept of signal	43	(5)
1.1.1 A few signals	44	(2)
1.1.2 Spectral representation of signals	46	(2)
1.2 The Concept of system	48	(2)
1.3 Summary	50	(1)
Chapter 2 Discrete Time Signals and Sampling	51	(30)
2.1 The sampling theorem	52	(13)
2.1.1 Perfect reconstruction	52	(12)
2.1.2 Digital-to-analog conversion	64	(1)
2.2 Plotting a signal as a function of time	65	(2)
2.3 Spectral representation	67	(10)
2.3.1 Discrete-time Fourier transform (DTFT)	67	(4)
2.3.2 Discrete Fourier transform (DFT)	71	(6)
2.4 Fast Fourier transform	77	(4)
Chapter 3 Spectral Observation	81	(20)
3.1 Spectral accuracy and resolution	81	(9)
3.1.1 Observation of a complex exponential	81	(2)
3.1.2 Plotting accuracy of the DTFT	83	(1)
3.1.3 Frequency resolution	84	(3)
3.1.4 Effects of windowing on the resolution	87	(3)
3.2 Short term Fourier transform	90	(4)
3.3 Summing up	94	(1)
3.4 Application examples and exercises	95	(6)
3.4.1 Amplitude modulations	95	(3)
3.4.2 Frequency modulation	98	(3)
Chapter 4 Linear Filters	101	(58)
4.1 Definitions and properties	101	(5)
4.2 The z-transform	106	(3)
4.2.1 Definition and properties	106	(1)
4.2.2 A few examples	107	(2)
4.3 Transforms and linear filtering	109	(2)
4.4 Difference equations and rational TF filters	111	(8)
4.4.1 Stability considerations	112	(2)
4.4.2 FIR and IIR filters	114	(1)
4.4.3 Causal solution and initial conditions	115	(2)
4.4.4 Calculating the responses	117	(1)
4.4.5 Stability and the Jury test	118	(1)
4.5 Connection between gain and poles/zeros	119	(10)
4.6 Minimum phase filters	129	(4)
4.7 Filter design methods	133	(17)
4.7.1 Going from the continuous-time filter to the discrete-time filter	133	(4)
4.7.2 FIR filter design using the window method	137	(10)
4.7.3 IIR filter design	147	(3)
4.8 Oversampling and undersampling	150	(9)
4.8.1 Oversampling	151	(4)
4.8.2 Undersampling	155	(4)
Chapter 5 Filter Implementation	159	(28)
5.1 Filter implementation	159	(14)
5.1.1 Examples of filter structures	159	(5)
5.1.2 Distributing the calculation load in an FIR filter	164	(1)
5.1.3 FIR block filtering	165	(2)
5.1.4 FFT filtering	167	(6)
5.2 Filter banks	173	(14)
5.2.1 Decimation and expansion	174	(3)
5.2.2 Filter banks	177	(10)
Chapter 6 An Introduction to Image Processing	187	(58)
6.1 Introduction	187	(9)
6.1.1 Image display, color palette	187	(4)
6.1.2 Importing images	191	(2)
6.1.3 Arithmetical and logical operations	193	(3)
6.2 Geometric transformations of an image	196	(7)
6.2.1 The typical transformations	196	(3)
6.2.2 Aligning images	199	(4)
6.3 Frequential content of an image	203	(4)
6.4 Linear filtering	207	(10)
6.5 Other operations on images	217	(19)
6.5.1 Undersampling	217	(1)
6.5.2 Oversampling	217	(3)
6.5.3 Contour detection	220	(6)
6.5.4 Median filtering	226	(1)
6.5.5 Maximum enhancement	227	(2)
6.5.6 Image binarization	229	(5)
6.5.7 Morphological filtering of binary images	234	(2)
6.6 JPEG lossy compression	236	(5)
6.6.1 Basic algorithm	236	(1)
6.6.2 Writing the compression function	237	(3)
6.6.3 Writing the decompression function	240	(1)
6.7 Watermarking	241	(6)
6.7.1 Spatial image watermarking	241	(3)
6.7.2 Spectral image watermarking	244	(1)
Part II Random Signals	245	(326)
Chapter 7 Random Variables	247	(26)
7.1 Random phenomena in signal processing	247	(1)
7.2 Basic concepts of random variables	248	(8)
7.3 Common probability distributions	256	(9)
7.3.1 Uniform probability distribution on (a, b)	256	(1)
7.3.2 Real Gaussian random variable	257	(1)
7.3.3 Complex Gaussian random variable	258	(1)
7.3.4 Generating the common probability distributions	259	(3)
7.3.5 Estimating the probability density	262	(1)
7.3.6 Gaussian random vectors	263	(2)
7.4 Generating an r.v. with any type of p.d.	265	(5)
7.5 Uniform quantization	270	(3)
Chapter 8 Random Processes	273	(44)
8.1 Introduction	273	(1)
8.2 Wide-sense stationary processes	274	(15)
8.2.1 Definitions and properties of WSS processes	275	(3)
8.2.2 Spectral representation of a WSS process	278	(7)
8.2.3 Sampling a WSS process	285	(4)
8.3 Estimating the covariance	289	(7)
8.4 Filtering formulae for WSS random processes	296	(6)
8.5 MA, AR and ARMA time series	302	(15)
8.5.1 Q order MA (Moving Average) process	302	(3)
8.5.2 P order AR (Autoregressive) Process	305	(7)
8.5.3 The Levinson algorithm	312	(3)
8.5.4 AR.MA (P, Q) process	315	(2)
Chapter 9 Continuous Spectra Estimation	317	(24)
9.1 Non-parametric estimation of the PSD	317	(12)
9.1.1 Estimation from the autocovariance function	317	(3)
9.1.2 Estimation based on the periodogram	320	(9)
9.2 Parametric estimation	329	(12)
9.2.1 AR estimation	329	(8)
9.2.2 Estimating the spectrum of an AR process	337	(1)
9.2.3 The Durbin method of MA estimation	338	(3)
Chapter 10 Discrete Spectra Estimation	341	(48)
10.1 Estimating the amplitudes and the frequencies	341	(6)
10.1.1 The case of a single complex exponential	341	(2)
10.1.2 Real harmonic mixtures	343	(2)
10.1.3 Complex harmonic mixtures	345	(2)
10.2 Periodograms and the resolution limit	347	(11)
10.3 High resolution methods	358	(31)
10.3.1 Periodic signals and recursive equations	358	(5)
10.3.2 The Prony method	363	(3)
10.3.3 The MUSIC algorithm	366	(13)
10.3.4 introduction to array processing	379	(10)
Chapter 11 The Least Squares Method	389	(62)
11.1 The projection theorem	389	(4)
11.2 The least squares method	393	(14)
11.2.1 Formulating the problem	393	(1)
11.2.2 The linear model	394	(1)
11.2.3 The least squares estimator	395	(7)
11.2.4 The RLS algorithm (recursive least squares)	402	(3)
11.2.5 Identifying the impulse response of a channel	405	(2)
11.3 Linear predictions of the WSS processes	407	(10)
11.3.1 Yule-Walker equations	407	(1)
11.3.2 Predicting a WSS harmonic process	408	(3)
11.3.3 Predicting a causal AR-P process	411	(1)
11.3.4 Reflection coefficients and lattice filters	412	(5)
11.4 Wiener filtering	417	(13)
11.4.1 Finite impulse response solution	419	(1)
11.4.2 Gradient algorithm	420	(7)
11.4.3 Wiener equalization	427	(3)
11.5 The LMS (least mean square) algorithm	430	(16)
11.5.1 The constant step algorithm	430	(9)
11.5.2 The normalized LMS algorithm	439	(3)
11.5.3 Echo canceling	442	(4)
11.6 Application: the Kalman algorithm	446	(5)
11.6.1 The Kalman filter	446	(3)
11.6.2 The vector case	449	(2)
Chapter 12 Selected Topics	451	(120)
12.1 Simulation of continuous-time systems	451	(4)
12.1.1 Simulation by approximation	451	(1)
12.1.2 Exact model simulation	452	(3)
12.2 Dual Tone Multi-Frequency (DTMF)	455	(6)
12.3 Speech processing	461	(10)
12.3.1 A speech signal model	461	(7)
12.3.2 Compressing a speech signal	468	(3)
12.4 DTW	471	(3)
12.5 Modifying the duration of an audio signal	474	(4)
12.5.1 PSOLA	475	(2)
12.5.2 Phase vocoder	477	(1)
12.6 Quantization noise shaping	478	(4)
12.7 Elimination of the background noise in audio	482	(2)
12.8 Eliminating the impulse noise	484	(6)
12.8.1 The signal model	484	(1)
12.8.2 Click detection	485	(3)
12.8.3 Restoration	488	(2)
12.9 Tracking the cardiac rhythm of the fetus	490	(11)
12.9.1 Objectives	490	(1)
12.9.2 Separating the EKG signals	491	(3)
12.9.3 Estimating cardiac rhythms	494	(7)
12.10 Extracting the contour of a coin	501	(2)
12.11 Principal component analysis (PCA)	503	(11)
12.11.1 Determining the principal components	503	(4)
12.11.2 2-Dimension PCA	507	(2)
12.11.3 Linear discriminant analysis (LDA)	509	(5)
12.12 Separating an instantaneous mixture	514	(2)
12.13 Matched filters in radar telemetry	516	(2)
12.14 Kalman filtering	518	(6)
12.15 Compression	524	(14)
12.15.1 Scalar quantization	524	(2)
12.15.2 Vector quantization	526	(12)
12.16 Digital communications	538	(24)
12.16.1 Introduction	538	(3)
12.16.2 8-phase shift keying (PSK)	541	(2)
12.16.3 PAM modulation	543	(2)
12.16.4 Spectrum of a digital signal	545	(4)
12.16.5 The Nyquist criterion in digital communications	549	(6)
12.16.6 The eye pattern	555	(1)
12.16.7 PAM modulation on the Nyquist channel	556	(6)
12.17 Linear equalization and the Viterbi algorithm	562	(11)
12.17.1 Linear equalization	564	(2)
12.17.2 The Viterbi algorithm	566	(5)
Part III Hints and Solutions	571	(156)
Chapter 13 Hints and Solutions	573	(154)
H1 Signal fundamentals	573	(1)
H2 Discrete time signals and sampling	573	(6)
H3 Spectral observation	579	(11)
H4 Linear filters	590	(20)
H5 Filter implementation	610	(4)
H6 An Introduction to image processing	614	(27)
H7 Random variables	641	(5)
H8 Random processes	646	(10)
H9 Continuous spectra estimation	656	(5)
H10 Discrete spectra estimation	661	(7)
H11 The least squares method	668	(8)
H12 Selected topics	676	(51)
Chapter 14 Appendix	727	(12)
A1 Fourier transform	727	(1)
A2 Discrete time Fourier transform	728	(1)
A3 Discrete Fourier transform	729	(1)
A4 z-Transform	730	(2)
A5 Jury criterion	732	(2)
A6 FFT filtering algorithms revisited	734	(5)
Bibliography	739	(8)
Index	747