GT Toán Cao cấp 2 – new (bản nháp)

On By hpdungIn Linear AlgebraLeave a comment

Chào các em sinh viên PTIT khối ngành KT, ĐPT,…

Đây là GT Toán Cao cấp 2 soạn theo đề cương mới nhé.

Link: https://drive.google.com/file/d/1D5JH_orTBLMI_Ub5KPvXuyQqbxwHS1XS/view?usp=sharing

Hoặc tải ở đây:

gt-toan-cao-cap-2-nhapDownload

Wavelets with applications in signal- and image processing

On By hpdungIn Advanced Engineering MathsLeave a comment

This is a course of Wavelet taught by Prof Adhemar Bultheel at KULeuven:

https://people.cs.kuleuven.be/~adhemar.bultheel/WWW/WAVE/contents.html

ps, pdf and zip on this page last modified: Thursday 26 October 2006, 08:07:19 AM CEST.
list of errata [ Last update: Tue May 22 19:00:07 CEST 2001 ]

Table of Contents (ps,pdf,zip)

This is the table of contents of the lecture notes.

  1. Introduction 1 (ps,pdf,zip)
  2. Signals 10 (ps,pdf,zip)
    1. Fourier transforms 10
    2. The time domain 13
      1. Digital signals 13
      2. Analog signals 14
    3. The frequency domain 16
      1. Digital signals 16
      2. Analog signals 18
    4. Sampling theorem 19
    5. Subsampling and upsampling of a discrete signal 22
    6. The Heisenberg uncertainty principle 24
    7. Time-frequency plane 26
    8. Summary 28
    9. Exercises 29
  3. Filters 32 (ps,pdf,zip)
    1. Definitions 32
    2. Inverse filter 34
    3. Bandpass filters 35
    4. QMF and PCF filters 38
    5. Exercises 38
  4. Filter banks 40 (ps,pdf,zip)
    1. Analysis and synthesis 40
    2. Perfect reconstruction 43
    3. Lossless filter bank 44
    4. Polyphase matrix 46
    5. Note on orthogonality 48
    6. Exercises 50
  5. Multiresolution 51 (ps,pdf,zip)
    1. Introduction 51
    2. Bases and frames 52
    3. Discrete versus continuous wavelet transform 55
    4. Definition of a multiresolution analysis 57
    5. The scaling function or father function 58
    6. Solution of the dilation equation 59
      1. Solution by iteration 60
      2. Solution by Fourier analysis 62
      3. Solution by recursion 63
      4. Solution by the cascade algorithm 64
    7. Properties of the scaling function 64
      1. General properties 65
      2. Orthogonality 67
    8. The wavelet or mother function 70
    9. Existence of the wavelet 72
    10. A more informal approach 75
    11. Summary 76
    12. Exercises 77
  6. Wavelet transform and filter banks 80 (ps,pdf,zip)
    1. Wavelet expansion and filtering 80
    2. Filter bank interpretation 84
    3. Fast Wavelet Transform 85
    4. Wavelets by linear algebra 89
    5. The wavelet crime 90
    6. Biorthogonal wavelets 91
    7. Semi-orthogonal wavelets 94
    8. Multi wavelets 95
    9. Exercises 96
  7. Approximating properties and wavelet design 97 (ps,pdf,zip)
    1. Smoothness 97
    2. Approximation 98
    3. Design properties: overview 99
    4. Some well known wavelets 99
      1. Haar wavelet 99
      2. Shannon or sinc wavelet 100
      3. Mexican hat function 100
      4. Morlet wavelet 101
      5. Meyer wavelet 101
      6. Daubechies maxflat wavelets 101
      7. Symlets 103
      8. Coiflets 104
      9. CDF or biorthogonal spline wavelets 105
    5. Battle-Lemarié wavelet 109
    6. Discrete versus continuous wavelet transforms revisited 110
    7. Overcomplete wavelet transform 111
    8. Redundant discrete wavelet transform 111
    9. Exercises 113
  8. Multidimensional wavelets 115 (ps,pdf,zip)
    1. Tensor product wavelets 115
    2. Nonseparable wavelets 118
    3. Examples of 2D CWT wavelets 121
      1. The 2D Mexican hat 122
      2. The 2D Morlet wavelet 122
  9. Subdivision and lifting 123 (ps,pdf,zip)
    1. In place Haar transform 123
    2. Interpolating subdivision 126
    3. Averaging subdivision 128
    4. Second generation wavelets 130
    5. Multiresolution 130
    6. The wavelets 132
    7. The lifting scheme 134
    8. The Euclidean algorithm 137
  10. Applications 145 (ps,pdf,zip)
    1. Signal processing 145
      1. NMR Spectroscopy 145
      2. Music and audio signals 146
      3. ECG signals 150
    2. Image processing 152
      1. Image compression 152
      2. Image denoising 156
    3. Wavelet modulation in communication channels 162
    4. Other applications 165
      1. Edge detection 166
      2. Contrast enhancement 166
      3. Texture analysis 167
      4. Computer graphics 169
      5. Numerical analysis 169
    5. Exercises 169
  11. Software and internet 171 (ps,pdf,zip)
  12. Bibliography (for this text) 172 (ps,pdf,zip)
  13. List of acronyms 174 + index (ps ,pdf,zip)
  14. Bibliography (books on wavelets)

The complete text as a zip archive (1.9M) ps (7.9M), pdf (1.7M).
Revised text with Daan Huybrechs (2011) pdf (2.0M).

Slides used in the lessons (pdf format): lesson 1 | lesson 2 | lesson 3 | lesson 4 | [Wednesday September 2006, 27 18:14:26 CEST]
Slides in printable version (pdf format): lesson 1 | lesson 2 | lesson 3 | lesson 4 | [Wednesday September 2006, 27 18:14:26 CEST]

GT Toán học ứng dụng trong ĐTVT

On By hpdungIn Advanced Engineering MathsLeave a comment

Các bạn học viên sử dụng Giáo trình này và giáo trình Xác suất thống kê của PTIT để học môn này nhé.

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