## Digital signal and image processing using MATLAB

#### Book Description:

This title provides the most important theoretical aspects of image and signal processing (ISP) for deterministic and random signals. The theory is supported by exercises and computer simulations relating to real applications. More than 200 programs and functions in the MATLAB® language, along with helpful comments and instructions, can be used to do numerical experiments. This helps readers learn more about this subject’s theoretical and practical parts.

Contents……Page 8
Preface……Page 16
Notations and Abbreviations……Page 20
Introduction to MATLAB……Page 24
1.1 Vectors and matrices……Page 25
1.2 Arrays……Page 27
1.3 Cells and structures……Page 28
2.1 Matrix operations……Page 30
2.2 Pointwise operations……Page 31
2.4 Predefined matrices……Page 32
2.5 Mathematical functions……Page 33
2.7 Other useful functions……Page 35
2.9 Program loops……Page 36
3. Graphically displaying results……Page 37
5. Input/output……Page 40
6. Program writing……Page 41
Part I: Deterministic Signals……Page 42
1.1 The concept of signal……Page 44
1.2 The Concept of system……Page 49
1.3 Summary……Page 51
Chapter 2: Discrete Time Signals and Sampling……Page 52
2.1 The sampling theorem……Page 53
2.2 Plotting a signal as a function of time……Page 66
2.3 Spectral representation……Page 68
2.4 Fast Fourier transform……Page 78
3.1 Spectral accuracy and resolution……Page 82
3.2 Short-term Fourier transform……Page 91
3.3 Summing up……Page 95
3.4 Application examples and exercises……Page 96
4.1 Definitions and properties……Page 102
4.2 The z-transform……Page 107
4.3 Transforms and linear filtering……Page 110
4.4 Difference equations and rational TF filters……Page 112
4.5 Connection between gain and poles/zeros……Page 120
4.6 Minimum phase filters……Page 130
4.7 Filter design methods……Page 134
4.8 Oversampling and undersampling……Page 151
5.1 Filter implementation……Page 160
5.2 Filter banks……Page 174
6.1 Introduction……Page 188
6.2 Geometric transformations of an image……Page 197
6.3 Frequential content of an image……Page 204
6.4 Linear filtering……Page 208
6.5 Other operations on images……Page 218
6.6 JPEG lossy compression……Page 237
6.7 Watermarking……Page 242
Part II: Random Signals……Page 246
7.1 Random phenomena in signal processing……Page 248
7.2 Basic concepts of random variables……Page 249
7.3 Common probability distributions……Page 257
7.4 Generating an r.v. with any type of p.d…….Page 266
7.5 Uniform quantization……Page 271
8.1 Introduction……Page 274
8.2 Wide-sense stationary processes……Page 275
8.3 Estimating the covariance……Page 290
8.4 Filtering formulae for WSS random processes……Page 297
8.5 MA, AR and ARMA time series……Page 303
9.1 Non-parametric estimation of the PSD……Page 318
9.2 Parametric estimation……Page 330
10.1 Estimating the amplitudes and the frequencies……Page 342
10.2 Periodograms and the resolution limit……Page 348
10.3 High resolution methods……Page 359
11.1 The projection theorem……Page 390
11.2 The least squares method……Page 394
11.3 Linear predictions of the WSS processes……Page 408
11.4 Wiener filtering……Page 418
11.5 The LMS (least mean square) algorithm……Page 431
11.6 Application: the Kalman algorithm……Page 447
12.1 Simulation of continuous-time systems……Page 452
12.2 Dual Tone Multi-Frequency (DTMF)……Page 456
12.3 Speech processing……Page 462
12.4 DTW……Page 472
12.5 Modifying the duration of an audio signal……Page 475
12.6 Quantization noise shaping……Page 479
12.7 Elimination of the background noise in audio……Page 483
12.8 Eliminating the impulse noise……Page 485
12.9 Tracking the cardiac rhythm of the fetus……Page 491
12.10 Extracting the contour of a coin……Page 502
12.11 Principal component analysis (PCA)……Page 504
12.12 Separating an instantaneous mixture……Page 515
12.13 Matched filters in radar telemetry……Page 517
12.14 Kalman filtering……Page 519
12.15 Compression……Page 525
12.16 Digital communications……Page 539
12.17 Linear equalization and the Viterbi algorithm……Page 563
Part III: Hints and Solutions……Page 572
H2. Discrete time signals and sampling……Page 574
H3. Spectral observation……Page 580
H4. Linear filters……Page 591
H5. Filter implementation……Page 611
H6. An Introduction to image processing……Page 615
H7. Random variables……Page 642
H8. Random processes……Page 647
H9. Continuous spectra estimation……Page 657
H10. Discrete spectra estimation……Page 662
H11. The least squares method……Page 669
H12. Selected topics……Page 677
A1. Fourier transform……Page 728
A2. Discrete time Fourier transform……Page 729
A3. Discrete Fourier transform……Page 730
A4. z-Transform……Page 731
A5. Jury criterion……Page 733
A6. FFT filtering algorithms revisited……Page 735

### Digital signal and image processing using MATLAB

#### Author(s): Gérard Blanchet, Maurice Charbit

Series: Digital signal and image processing series

Publisher: ISTE Ltd, Year: 2006

ISBN: 9781905209132