Conceptual Wavelets in Digital Signal Processing pdf epub mobi txt 电子书 下载 2026
出版者:Space & Signals Technical Publishing
作者:D. Lee Fugal
出品人:
页数:374
译者:
出版时间:2009-7-1
价格:USD 125.00
装帧:
isbn号码:9780982199459
丛书系列:
图书标签:
- 实验语音学
- 信号处理
- Wavelets
- Digital Signal Processing
- Signal Analysis
- Time-Frequency Analysis
- Mathematical Methods
- Engineering
- Applied Mathematics
- Data Analysis
- Image Processing
- Communications
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具体描述
数字信号处理中的高级滤波器设计与应用 本书深入探讨了现代数字信号处理领域中，特别是针对非线性系统建模、自适应滤波理论及其在复杂环境下的实际应用所涉及的前沿技术与理论框架。它并非专注于小波分析的特定数学结构，而是将重点放在了信号处理的统计学基础、优化方法以及系统辨识上，为读者提供一个超越传统线性滤波方法的广阔视角。 第一部分：非线性系统的理论基础与建模 本部分首先对数字信号处理的数学基础进行了回顾，但很快就将重点转向了非线性系统的建模挑战。传统的FIR/IIR滤波器在处理高斯白噪声以外的复杂干扰、非平稳信号或具有明显非线性特征的系统时，其性能会急剧下降。 我们详细阐述了Volterra级数展开在描述有限记忆非线性系统中的作用。本书不仅推导了Volterra滤波器的结构，更着重分析了高阶项的计算复杂性与参数估计难度。随后，引入了多项式滤波与反馈结构，探讨如何利用这些结构来近似任意连续函数，并讨论了在有限数据量下避免维度灾难的有效策略。 特别关注了神经结构在信号处理中的应用。我们详细分析了前馈神经网络（FNN）和循环神经网络（RNN）的简化版本如何作为非线性函数逼近器，应用于信道均衡、噪声抑制和系统辨识。本书强调了激活函数的选择对收敛速度和最终性能的影响，并提供了基于梯度下降的权重更新算法的实际操作指南，而非仅仅停留在理论推导。 第二部分：自适应滤波理论的深度剖析 自适应滤波器是处理时变环境和未知系统特性的核心工具。本书在标准LMS算法的基础上，进行了大量的扩展和深化。 LMS及其变体的优化： 我们对最小均方（LMS）算法的收敛性、稳态误差进行了详尽的分析，并深入探讨了归一化LMS（NLMS）如何通过动态步长调整来克服输入信号功率变化带来的问题。随后，引入了比例LMS（PLMS）和投影梯度算法，重点讨论了它们在收敛速度与复杂度之间的权衡。 次梯度优化方法： 针对信号中存在脉冲噪声或大瞬时误差的情况，LMS算法的性能不佳。本书详细介绍了次梯度优化算法，特别是符号函数最小化（SF-LMS）和基于次梯度的算法（Sign-Sign LMS）。这些算法的优势在于对噪声的鲁棒性，尽管它们通常以较慢的最终收敛速度为代价。我们提供了详细的收敛性证明框架和实际应用案例，例如在音频降噪中的应用。 基于度量的自适应算法： 跳出传统的L2范数误差最小化，本书探索了基于更鲁棒误差度量的自适应滤波器设计，例如最小化P范数误差或采用M估计的滤波器。这对于在存在粗差（Outliers）的环境中进行信号分离至关重要。 第三部分：高级应用与系统辨识 第三部分将理论与实际工程问题紧密结合，展示了如何将前面介绍的非线性建模和自适应技术应用于复杂的信号处理场景。 盲源分离（BSS）的非线性扩展： 在传统的独立分量分析（ICA）主要基于线性混合模型的背景下，本书着重探讨了非线性盲源分离的挑战。我们介绍了如何将信息论准则（如互信息）与非线性映射相结合，构建可用于分离非高斯、非线性混合信号的迭代优化框架。 系统辨识与状态估计： 针对工业过程控制和通信系统中的非线性系统辨识，我们详细阐述了扩展卡尔曼滤波（EKF）和无迹卡尔曼滤波（UKF）的应用。EKF通过一阶泰勒展开对非线性函数进行线性化近似，而UKF采用Sigma点采样方法，能够更精确地捕捉非线性系统的均值和协方差演变。本书提供了这两种滤波器的实现细节，并对比了它们在估计非线性系统状态时的精度和计算负担。 无线信道建模与均衡： 在移动通信领域，多径效应和时变特性导致信道具有显著的非平稳和非线性特征。本书展示了如何利用自适应Volterra均衡器来补偿信道中的记忆效应和饱和非线性，并与传统的线性预编码技术进行了性能对比。特别关注了信道状态信息（CSI）实时估计的自适应算法设计。 结论与展望： 本书的最终目标是使读者能够根据具体的信号特性和环境约束，选择或设计出最适合的非线性或自适应处理方案。它强调了数学严谨性与工程实践的结合，为后续深入研究复杂信号的统计特性和高级优化方法奠定了坚实的基础。本书的结构旨在引导读者从经典的线性处理思维中解放出来，全面掌握现代信号处理中应对复杂性和不确定性的工具箱。
作者简介
目录信息
CONTENTS
Preface...................................................................................................................................xiii
Understanding & Harnessing Wavelet “Elephants”..........................................................xiii
How this Book Differs from Other Wavelet Texts............................................................xv
How this Book is Laid Out—Study Suggestions..............................................................xvi
Acknowledgments................................................................................................................xxi
1
Preview of Wavelets, Wavelet Filters, and Wavelet Transforms..................................1
1.1 What is a Wavelet?.........................................................................................................2
1.2 What is a Wavelet Filter and how is it different from a Wavelet?..................................3
1.3 The value of Transforms and Examples of Everyday Use.............................................6
1.4 Short-Time Transforms, Sheet Music, and a first look at Wavelet Transforms............8
1.5 Example of the Fast Fourier Transform (FFT) with an Embedded Pulse Signal.........11
1.6 Examples using the Continuous Wavelet Transform...................................................13
1.7 A First Glance at the Undecimated Discrete Wavelet Transform (UDWT)................19
1.8 A First Glance at the conventional Discrete Wavelet Transform (DWT)...................24
1.9 Examples of use of the conventional DWT..................................................................27
1.10 Summary....................................................................................................................29
2
The Continuous Wavelet Transform (CWT) Step-by-Step........................................31
2.1 Simple Scenario: Comparing Exam Scores using the Haar Wavelet..............................31
2.2 Above Comparison Process seen as simple Correlation or Convolution.....................34
2.3 CWT Display of the Exam Scores using the Haar Wavelet Filter................................37
2.4 Summary......................................................................................................................41
3
The Undecimated Discrete Wavelet Transform (UDWT) Step-by-Step...................43
3.1 Single-Level Undecimated Discrete Wavelet Transform (UDWT) of Exam Data.......43
3.2 Frequency Allocation of a Single-Level UDWT..........................................................46
3.3 Multi-Level Undecimated Discrete Wavelet Transform (UDWT)..............................49
3.4 Frequency Allocation of a Multiple-Level UDWT.....................................................53
3.5 The Haar UDWT as a Moving Averager.....................................................................56
3.6 Summary......................................................................................................................57
4
The Conventional (Decimated) DWT Step-by-Step....................................................59
4.1 Single-Level (Decimated) Discrete Wavelet Transform (DWT) of Exam Data............59
4.2 Additional Example of Perfect Reconstruction in a Single-Level DWT.......................63
4.3 Compression and Denoising Example using the Single-Level DWT............................64
4.4 Multi-Level Conventional (Decimated) DWT of Exam Data using Haar Filters.........65
4.5 Frequency Allocation in a (Conventional, Decimated) DWT......................................68
4.6 Final Approximations and Details and how to read the DWT Display......................70
4.7 Denoising using a Multi-Level DWT...........................................................................72
4.8 Summary......................................................................................................................77
5
Obtaining Discrete Wavelet Filters from “Crude” Wavelet Equations....................79
5.1 Review of Familiar DSP Truncated Sinc Function.......................................................79
5.2 Adding More Points at the Ends for Better Filter Performance..................................80
5.3 Adding More Points by Interpolation for Lower Cutoff Frequency...........................82
5.4 Multi-Point Stretched Filters (“Crude Wavelets”) from Explicit Equations...............83
5.5 Mexican Hat Wavelet Filter as an Example of a Stretched Crude Filter......................84
5.6 Morlet Wavelet as another example of Stretched Crude Filters...................................90
5.7 Bandpass Characteristics of the Mexican Hat and Morlet Wavelet Filters.................94
5.8 Summary......................................................................................................................98
6
Obtaining Variable Length Filters from Basic Fixed Length Filters.....................101
6.1 Review of Conventional Interpolation Techniques from DSP...................................101
6.2 Interpolating the Basic “Mother” Wavelet by Upsampling and Lowpass Filtering..106
6.3 Frequency Characteristics of the Basic and Stretched Haar Filters...........................110
6.4 Perfect Overlay of Filter Points on the “Continuous” Wavelet Estimation..............114
6.5 Frequency Characteristics of some of the Basic Filters.............................................117
6.6 Summary....................................................................................................................119
7
Comparison of the Major Types of Wavelet Transforms..........................................121
7.1 Advantages and Disadvantages of the Continuous Wavelet Transform....................121
7.2 Stretching the Wavelet—The Undecimated Discrete Wavelet Transform.................124
7.3 Shrinking the Signal—The Conventional Discrete Wavelet Transform.....................129
7.4 Relating the Conventional DWT to the Continuous Wavelet Transform..................135
7.5 Decomposing All the Frequencies—The Wavelet Packet Transform........................137
7.6 Summary....................................................................................................................140
8
PRQMF and Halfband Filters and How they are Related.........................................141
8.1 Perfect Reconstruction Quadrature Mirror Filters and their Inter-Relationships......141
8.2 Perfect Reconstruction Begins with the Halfband Filters..........................................144
8.3 Properties of the Halfband Filters..............................................................................147
8.4 “Reverse Engineering” Perfect Reconstruction to Produce the Basic Filters.............150
8.5 Orthogonal Vectors, Sinusoids, and Wavelets............................................................155
8.6 Biorthogonal Filters—Another Way to Factor the Halfband Filters.........................161
8.7 Summary....................................................................................................................167
9
Highlighting Additional Properties by using “Fake” Wavelets...............................169
9.1 Matching the Wavelet to the Signal and the Concept of Regularity..........................169
9.2 Customized Wavelets, Best Basis, and the “Sport of Basis Hunting”......................174
9.3 Vanishing Moments and another Fake Wavelet.........................................................175
9.4 Examples of Use of Vanishing Moments...................................................................178
9.5 Finding the “Magic Numbers” of Basic Db4 Filters using Wavelet Properties.........183
9.6 Summary....................................................................................................................184
10 Specific Properties and Applications of Wavelet Families.......................................187
10.1 (Real) Crude Wavelets..............................................................................................188
MEXICAN HAT WAVELET .......................................................................................189
MORLET WAVELET .................................................................................................190
GAUSSIAN WAVELETS ............................................................................................191
MEYER WAVELETS .................................................................................................192
10.2 Complex Crude Wavelets.........................................................................................194
SHANNON (“SINC”) WAVELET.................................................................................194
COMPLEX FREQUENCY B-SPLINE WAVELETS .......................................................198
COMPLEX MORLET WAVELET ................................................................................201
COMPLEX GAUSSIAN WAVELETS ...........................................................................201
10.3 Orthogonal Wavelets................................................................................................203
HAAR WAVELETS....................................................................................................204
DAUBECHIES WAVELETS .......................................................................................205
SYMLETS .................................................................................................................207
COIFLETS ................................................................................................................209
DISCRETE MEYER WAVELETS ...............................................................................211
10.4 Biorthogonal and Reverse Biorthogonal Wavelets...................................................214
BIORTHOGONAL WAVELETS...................................................................................214
REVERSE BIORTHOGONAL WAVELETS..................................................................216
10.5 Summary and Table of Wavelets and their Properties.............................................217
TABLE 10.5–1 - ATTRIBUTES OF THE VARIOUS WAVELETS (FILTERS) .................219
11 Case Studies of Wavelet Applications.........................................................................221
11.1 White Noise in a Chirp Signal..................................................................................221
11.2 Binary Signal Buried in Chirp Noise........................................................................225
11.3 Binary Signal with White Noise...............................................................................230
11.4 Image Compression/De-noising................................................................................236
11.5 Improved Performance using the UDWT................................................................241
11.6 Summary..................................................................................................................249
12 Alias Cancellation in the Conventional (Decimated) DWT....................................251
12.1 DWT Alias Cancellation Demonstrated in the Time Domain..................................251
12.2 DWT Alias Cancellation Demonstrated in the Frequency Domain.........................261
12.3 Relating the Above Concepts to Equations Found in the Traditional Literature.....271
12.4 Summary..................................................................................................................278
13 Relating Key Equations to Conceptual Understanding............................................281
13.1 Building the Scaling Function from The “Dilation Equation”..................................281
13.2 Building the Scaling Function Using Upsampling and Simple Convolution............288
13.3 Building the Wavelet Function from the Dilation Equation.....................................291
13.4 Building the Wavelet Function Using Upsampling and Simple Convolution..........294
13.5 “Forward DWT”, “Inverse DWT” and Other Terms from Wavelet Literature.......296
13.6 Summary..................................................................................................................299
Postscript...............................................................................................................................301
Appendix A: Relating Wavelet Transforms to Fourier Transforms...............................A1
A.1 Example of a Pathological Case Using the Fast Fourier Transform...........................A1
A.2 FFT and STFT Results Shown In Continuous Wavelet Transform Format.............A2
A.3 The Wavelet Terms “Approximation” and “Details” Shown in FFT Format...........A4
A.4 The FFT Presented as a Sinusoid Correlation (Similar to Wavelet Correlation)........A6
A.5 The Ordinary Acoustic Piano: An Audio Fourier Transform..................................A12
Appendix B: Heisenberg Boxes and the Heisenberg Uncertainty Principle.................B1
B.1 Natural Order of Time and Frequency.......................................................................B1
B.2 Heisenberg Boxes (Cells) and the Uncertainty Principle............................................B2
B.3 Short Time Fourier Transforms are Constrained to Fixed Heisenberg Boxes............B3
© 2009 Space & Signals Technologies LLC, All Rights Reserved. www.ConceptualWavelets.com
Appendix C: Reprint of Article “Wavelets: Beyond Comparison”.................................C1
The Discrete Fourier Transform/Fast Fourier Transform (DFT/FFT).............................C1
The Continuous Wavelet Transform (CWT)....................................................................C3
Discrete Wavelet Transforms Overview...........................................................................C7
Undecimated or “Redundant” Discrete Wavelet Transforms (UDWT/RDWT)..............C8
Conventional (Decimated) Discrete Conventional Transforms (DWT)...........................C8
Appendix D: Further Resources for the Study of Wavelets.............................................D1
D.1 Wavelet Books...........................................................................................................D2
D.2 Wavelet Articles.........................................................................................................D6
D.3 Wavelet Websites.......................................................................................................D8
Index.......................................................................................................................................I 1
· · · · · · (收起)
Preface...................................................................................................................................xiii
Understanding & Harnessing Wavelet “Elephants”..........................................................xiii
How this Book Differs from Other Wavelet Texts............................................................xv
How this Book is Laid Out—Study Suggestions..............................................................xvi
Acknowledgments................................................................................................................xxi
1
Preview of Wavelets, Wavelet Filters, and Wavelet Transforms..................................1
1.1 What is a Wavelet?.........................................................................................................2
1.2 What is a Wavelet Filter and how is it different from a Wavelet?..................................3
1.3 The value of Transforms and Examples of Everyday Use.............................................6
1.4 Short-Time Transforms, Sheet Music, and a first look at Wavelet Transforms............8
1.5 Example of the Fast Fourier Transform (FFT) with an Embedded Pulse Signal.........11
1.6 Examples using the Continuous Wavelet Transform...................................................13
1.7 A First Glance at the Undecimated Discrete Wavelet Transform (UDWT)................19
1.8 A First Glance at the conventional Discrete Wavelet Transform (DWT)...................24
1.9 Examples of use of the conventional DWT..................................................................27
1.10 Summary....................................................................................................................29
2
The Continuous Wavelet Transform (CWT) Step-by-Step........................................31
2.1 Simple Scenario: Comparing Exam Scores using the Haar Wavelet..............................31
2.2 Above Comparison Process seen as simple Correlation or Convolution.....................34
2.3 CWT Display of the Exam Scores using the Haar Wavelet Filter................................37
2.4 Summary......................................................................................................................41
3
The Undecimated Discrete Wavelet Transform (UDWT) Step-by-Step...................43
3.1 Single-Level Undecimated Discrete Wavelet Transform (UDWT) of Exam Data.......43
3.2 Frequency Allocation of a Single-Level UDWT..........................................................46
3.3 Multi-Level Undecimated Discrete Wavelet Transform (UDWT)..............................49
3.4 Frequency Allocation of a Multiple-Level UDWT.....................................................53
3.5 The Haar UDWT as a Moving Averager.....................................................................56
3.6 Summary......................................................................................................................57
4
The Conventional (Decimated) DWT Step-by-Step....................................................59
4.1 Single-Level (Decimated) Discrete Wavelet Transform (DWT) of Exam Data............59
4.2 Additional Example of Perfect Reconstruction in a Single-Level DWT.......................63
4.3 Compression and Denoising Example using the Single-Level DWT............................64
4.4 Multi-Level Conventional (Decimated) DWT of Exam Data using Haar Filters.........65
4.5 Frequency Allocation in a (Conventional, Decimated) DWT......................................68
4.6 Final Approximations and Details and how to read the DWT Display......................70
4.7 Denoising using a Multi-Level DWT...........................................................................72
4.8 Summary......................................................................................................................77
5
Obtaining Discrete Wavelet Filters from “Crude” Wavelet Equations....................79
5.1 Review of Familiar DSP Truncated Sinc Function.......................................................79
5.2 Adding More Points at the Ends for Better Filter Performance..................................80
5.3 Adding More Points by Interpolation for Lower Cutoff Frequency...........................82
5.4 Multi-Point Stretched Filters (“Crude Wavelets”) from Explicit Equations...............83
5.5 Mexican Hat Wavelet Filter as an Example of a Stretched Crude Filter......................84
5.6 Morlet Wavelet as another example of Stretched Crude Filters...................................90
5.7 Bandpass Characteristics of the Mexican Hat and Morlet Wavelet Filters.................94
5.8 Summary......................................................................................................................98
6
Obtaining Variable Length Filters from Basic Fixed Length Filters.....................101
6.1 Review of Conventional Interpolation Techniques from DSP...................................101
6.2 Interpolating the Basic “Mother” Wavelet by Upsampling and Lowpass Filtering..106
6.3 Frequency Characteristics of the Basic and Stretched Haar Filters...........................110
6.4 Perfect Overlay of Filter Points on the “Continuous” Wavelet Estimation..............114
6.5 Frequency Characteristics of some of the Basic Filters.............................................117
6.6 Summary....................................................................................................................119
7
Comparison of the Major Types of Wavelet Transforms..........................................121
7.1 Advantages and Disadvantages of the Continuous Wavelet Transform....................121
7.2 Stretching the Wavelet—The Undecimated Discrete Wavelet Transform.................124
7.3 Shrinking the Signal—The Conventional Discrete Wavelet Transform.....................129
7.4 Relating the Conventional DWT to the Continuous Wavelet Transform..................135
7.5 Decomposing All the Frequencies—The Wavelet Packet Transform........................137
7.6 Summary....................................................................................................................140
8
PRQMF and Halfband Filters and How they are Related.........................................141
8.1 Perfect Reconstruction Quadrature Mirror Filters and their Inter-Relationships......141
8.2 Perfect Reconstruction Begins with the Halfband Filters..........................................144
8.3 Properties of the Halfband Filters..............................................................................147
8.4 “Reverse Engineering” Perfect Reconstruction to Produce the Basic Filters.............150
8.5 Orthogonal Vectors, Sinusoids, and Wavelets............................................................155
8.6 Biorthogonal Filters—Another Way to Factor the Halfband Filters.........................161
8.7 Summary....................................................................................................................167
9
Highlighting Additional Properties by using “Fake” Wavelets...............................169
9.1 Matching the Wavelet to the Signal and the Concept of Regularity..........................169
9.2 Customized Wavelets, Best Basis, and the “Sport of Basis Hunting”......................174
9.3 Vanishing Moments and another Fake Wavelet.........................................................175
9.4 Examples of Use of Vanishing Moments...................................................................178
9.5 Finding the “Magic Numbers” of Basic Db4 Filters using Wavelet Properties.........183
9.6 Summary....................................................................................................................184
10 Specific Properties and Applications of Wavelet Families.......................................187
10.1 (Real) Crude Wavelets..............................................................................................188
MEXICAN HAT WAVELET .......................................................................................189
MORLET WAVELET .................................................................................................190
GAUSSIAN WAVELETS ............................................................................................191
MEYER WAVELETS .................................................................................................192
10.2 Complex Crude Wavelets.........................................................................................194
SHANNON (“SINC”) WAVELET.................................................................................194
COMPLEX FREQUENCY B-SPLINE WAVELETS .......................................................198
COMPLEX MORLET WAVELET ................................................................................201
COMPLEX GAUSSIAN WAVELETS ...........................................................................201
10.3 Orthogonal Wavelets................................................................................................203
HAAR WAVELETS....................................................................................................204
DAUBECHIES WAVELETS .......................................................................................205
SYMLETS .................................................................................................................207
COIFLETS ................................................................................................................209
DISCRETE MEYER WAVELETS ...............................................................................211
10.4 Biorthogonal and Reverse Biorthogonal Wavelets...................................................214
BIORTHOGONAL WAVELETS...................................................................................214
REVERSE BIORTHOGONAL WAVELETS..................................................................216
10.5 Summary and Table of Wavelets and their Properties.............................................217
TABLE 10.5–1 - ATTRIBUTES OF THE VARIOUS WAVELETS (FILTERS) .................219
11 Case Studies of Wavelet Applications.........................................................................221
11.1 White Noise in a Chirp Signal..................................................................................221
11.2 Binary Signal Buried in Chirp Noise........................................................................225
11.3 Binary Signal with White Noise...............................................................................230
11.4 Image Compression/De-noising................................................................................236
11.5 Improved Performance using the UDWT................................................................241
11.6 Summary..................................................................................................................249
12 Alias Cancellation in the Conventional (Decimated) DWT....................................251
12.1 DWT Alias Cancellation Demonstrated in the Time Domain..................................251
12.2 DWT Alias Cancellation Demonstrated in the Frequency Domain.........................261
12.3 Relating the Above Concepts to Equations Found in the Traditional Literature.....271
12.4 Summary..................................................................................................................278
13 Relating Key Equations to Conceptual Understanding............................................281
13.1 Building the Scaling Function from The “Dilation Equation”..................................281
13.2 Building the Scaling Function Using Upsampling and Simple Convolution............288
13.3 Building the Wavelet Function from the Dilation Equation.....................................291
13.4 Building the Wavelet Function Using Upsampling and Simple Convolution..........294
13.5 “Forward DWT”, “Inverse DWT” and Other Terms from Wavelet Literature.......296
13.6 Summary..................................................................................................................299
Postscript...............................................................................................................................301
Appendix A: Relating Wavelet Transforms to Fourier Transforms...............................A1
A.1 Example of a Pathological Case Using the Fast Fourier Transform...........................A1
A.2 FFT and STFT Results Shown In Continuous Wavelet Transform Format.............A2
A.3 The Wavelet Terms “Approximation” and “Details” Shown in FFT Format...........A4
A.4 The FFT Presented as a Sinusoid Correlation (Similar to Wavelet Correlation)........A6
A.5 The Ordinary Acoustic Piano: An Audio Fourier Transform..................................A12
Appendix B: Heisenberg Boxes and the Heisenberg Uncertainty Principle.................B1
B.1 Natural Order of Time and Frequency.......................................................................B1
B.2 Heisenberg Boxes (Cells) and the Uncertainty Principle............................................B2
B.3 Short Time Fourier Transforms are Constrained to Fixed Heisenberg Boxes............B3
© 2009 Space & Signals Technologies LLC, All Rights Reserved. www.ConceptualWavelets.com
Appendix C: Reprint of Article “Wavelets: Beyond Comparison”.................................C1
The Discrete Fourier Transform/Fast Fourier Transform (DFT/FFT).............................C1
The Continuous Wavelet Transform (CWT)....................................................................C3
Discrete Wavelet Transforms Overview...........................................................................C7
Undecimated or “Redundant” Discrete Wavelet Transforms (UDWT/RDWT)..............C8
Conventional (Decimated) Discrete Conventional Transforms (DWT)...........................C8
Appendix D: Further Resources for the Study of Wavelets.............................................D1
D.1 Wavelet Books...........................................................................................................D2
D.2 Wavelet Articles.........................................................................................................D6
D.3 Wavelet Websites.......................................................................................................D8
Index.......................................................................................................................................I 1
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翻阅《Conceptual Wavelets in Digital Signal Processing》的过程中，我越发觉得这本书的价值所在，尤其是在数字信号处理领域。我一直坚信，在掌握复杂的数学工具时，建立起坚实的“概念”基础是至关重要的。这本书的标题就点明了这一点，它承诺的是一种深入的、概念性的理解，而不是停留在表面的公式记忆。我非常期待书中能够清晰地阐述小波变换的核心思想，比如它如何能够同时实现高时间分辨率和高频率分辨率，并且如何通过多尺度分析来捕捉信号在不同分辨率上的特征。我尤其好奇书中会如何解释小波基函数的性质，以及不同类型的母小波（mother wavelet）是如何工作的，以及它们各自的优缺点。如果书中能够提供一些富有洞察力的类比，例如将小波看作是“在信号上滑动并改变大小的探测器”，或者用“不同分辨率的滤镜组”来比喻多分辨率分析，那将极大地帮助我构建深刻的理解。
评分这本《Conceptual Wavelets in Digital Signal Processing》给我留下了深刻的印象，尽管我还没有深入阅读其中的每一章，但从书的整体构架和初步翻阅来看，它似乎是一本非常宝贵的技术参考资料。我尤其关注其在数字信号处理领域引入小波概念的处理方式。我一直觉得，在理解复杂的信号处理算法时，直观的物理模型和概念性的解释至关重要。这本书的书名就暗示了它将专注于“概念”，这对于我这样希望深入理解技术背后原理的读者来说，无疑是巨大的吸引力。我希望能找到书中能够清晰阐述小波变换如何打破传统傅里叶变换在时频分辨率上的局限性，以及它如何巧妙地将信号分解成不同尺度和位置的子分量，从而提供更丰富的信号信息。我对于小波在图像压缩、噪声去除、特征提取等方面的应用非常感兴趣，如果书中能提供一些生动形象的类比或案例，那就更好了。例如，它是否会用类似于“放大镜”或“显微镜”的概念来解释多分辨率分析？或者用“不同频率的音叉”来比喻小波基函数？我对这些概念性的讲解充满期待，希望它能帮助我建立起对小波理论的坚实基础，而不仅仅是记住一堆公式。
评分在阅读《Conceptual Wavelets in Digital Signal Processing》的过程中，我深刻体会到了概念理解的重要性，即便我还没有完全掌握其全部精髓。这本书以其独特的视角，将抽象的小波理论与实际的数字信号处理应用紧密结合，为我打开了一扇新的大门。我尤其欣赏它对小波概念的深入阐释，它不仅仅是罗列公式，而是试图构建一个直观的理解框架。我希望这本书能够帮助我理解小波变换为何能够克服傅里叶变换在处理非平稳信号时存在的局限性，以及它如何通过多分辨率分析提供更丰富的时频信息。我对于书中如何解释小波基函数的选取和设计非常好奇，以及这些选择如何影响信号分析的结果。如果书中能提供一些生动的例子，例如用“动态的尺子”来形容小波在时频窗口上的移动，或者用“不同频率的弹簧”来比喻小波的尺度变化，那将非常有帮助。
评分我最近刚拿到这本《Conceptual Wavelets in Digital Signal Processing》，尽管我可能还没有机会全面地深入研究，但第一印象就非常棒。我特别欣赏它在开篇就着重于“概念”的这一取向。我一直认为，许多技术书籍在讲解复杂的数学工具时，往往会过早地陷入公式推导，而忽略了对核心思想的阐释，这对于初学者或者希望从更宏观角度理解问题的读者来说，是一大障碍。这本书的标题正好抓住了我的痛点，它承诺的是一种“概念性”的理解，而不是纯粹的数学证明。我期待它能够用一种循序渐进、易于理解的方式，介绍小波分析的基本思想，比如它如何能够同时捕捉信号的频率和时间信息，这是傅里叶变换所不具备的。我尤其好奇书中会如何解释小波基函数的选择，以及不同的母小波（mother wavelet）会对信号分析产生怎样的影响。如果书中能够提供一些图示或者类比，比如将小波看作是“不同大小的窗户”在信号上滑动，这样能够更直观地理解其时频分析的优势。我希望这本书能够帮助我建立起对小波理论的直观感受，而不是仅仅停留在公式层面。
评分我手头的这本《Conceptual Wavelets in Digital Signal Processing》给我带来了极大的启发，尽管我还在慢慢消化其中的内容，但我已经能感受到它在数字信号处理领域的重要性。我一直觉得，对于像小波变换这样强大但又相对抽象的工具，一个清晰、直观的概念框架是多么重要。这本书的书名就直接点明了其核心——“概念”，这正是我一直在寻找的。我希望通过这本书，能够真正理解小波变换是如何在时频域上提供比传统方法（如短时傅里叶变换）更精细的分辨率，以及它如何通过多分辨率分析来揭示信号在不同尺度上的结构。我非常期待书中能够深入探讨小波在信号去噪、特征提取、以及图像处理等方面的应用，并用易于理解的语言解释其背后的原理。例如，书中是否会用“逐层剥洋葱”的比喻来形容信号的多尺度分解？或者将小波基函数比作“适应性搜索工具”，能够根据信号的局部特性进行调整？这些类比对于构建深刻的理解至关重要。
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