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"Nature laughs at the difficulties of integration" - Pierre-Simon de Laplace
طبيعت مسائل مشکل رياضی را به سخره می گيرد! (سیمون لاپلاس)
در بيشتر زمينه های علمی، نقش رياضیات ایجاد مدل هایی دقيق و قابل بررسی برای پديده های فيزیکی است و اين ابزار کارآمد امکان مطالعه ی کمی و پیش بینی پدیده ها ی طبيعی را به انسان می دهد. با اين وجود در شرايطی که به برخی زمینه های کاربردی در مهندسی، به ابزارهای ریاضی به ديده ای صلب و کاربردی نگریسته شود امکان درک شهودی و در نتیجه ایجاد خلاقیت از محقق سلب شده و استعدادهای بالقوه کمتر مجال بروز می یابند.
نوشته ی فوق مقدمه ای بود برای ترغیب دوست داران ریاضیات زنده به مطالعه ی کتاب ارزنده ی:
The Scientist and Engineer's Guide to
Digital Signal Processing
در اين کتاب که تمام فصول آن به رايگان در اینترنت منشر شده، مولف کوشيده است تا با ايجاد دیدگاهی بنیادی مطالب عمدتا سنگین پردازش سیگنال دیجیتال یا DSP را از زوایای فیزیکی به خواننده تفهیم کند. 13 فصل ابتدایی این کتاب مباحث مربوط به سیگنال سیستم و همچنين پیش نیارهای پردازش سیگنال دیجیتال را با زبانی شیوا پوشش داده و بعد از آن تا فصل 21 ام فیلتر دیجیتال به تفصیل بحث شده است. 8 فصل بعد آن شامل مباحث کاربردی از قبیل: پردازش صوت و تصویر، شبکه های عصبی، فشرده سازی اطلاعات و غیره می باشد. 4 فصل پایانی که به نوعی ادامه ی 13 فصل ابتدایی می باشند، ابزارهای پردازش را در حوزه ی اعداد مختلط پوشش می دهند.
لیست فصول در زیر آورده شده است.
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Chapter 1. The Breadth and Depth of DSP
The Roots of DSP 1
Telecommunications 4
Audio Processing 5
Echo Location 7
Imaging Processing 9
Chapter 2. Statistics, Probability and Noise
Signal and Graph Terminology 11
Mean and Standard Deviation 13
Signal vs. Underlying Process 17
The Histogram, Pmf and Pdf 19
The Normal Distribution 26
Digital Noise Generation 29
Precision and Accuracy 32
Chapter 3. ADC and
Quantization 35
The Sampling Theorem 39
Digital-to-Analog Conversion 44
Analog Filters for Data Conversion 48
Selecting the Antialias Filter 55
Multirate Data Conversion 58
Single Bit Data Conversion 60
Chapter 4. DSP
Computer Numbers 67
Fixed Point (Integers) 68
Floating Point (Real Numbers) 70
Number Precision 72
Execution Speed: Program Language 76
Execution Speed: Hardware 80
Execution Speed: Programming Tips 84
Chapter 5. Linear Systems
Signals and Systems 87
Requirements for Linearity 89
Static Linearity and Sinusoidal Fidelity 92
Examples of Linear and Nonlinear Systems 94
Special Properties of Linearity 96
Superposition: the Foundation of DSP 98
Common Decompositions 100
Alternatives to Linearity 104
Chapter 6. Convolution
The Delta Function and Impulse Response 107
Convolution 108
The Input Side Algorithm 112
The Output Side Algorithm 116
The Sum of Weighted Inputs 122
Chapter 7. Properties of Convolution
Common Impulse Responses 123
Mathematical Properties 132
Correlation 136
Speed 140
Chapter 8. The Discrete Fourier Transform
The Family of Fourier Transforms 141
Notation and Format of the real DFT 146
The Frequency Domain's Independent Variable 148
DFT Basis Functions 150
Synthesis, Calculating the Inverse DFT 152
Analysis, Calculating the DFT 156
Duality 161
Polar Notation 161
Polar Nuisances 164
Chapter 9. Applications of the DFT
Spectral Analysis of Signals 169
Frequency Response of Systems 177
Convolution via the Frequency Domain 180
Chapter 10. Fourier Transform Properties
Linearity of the Fourier Transform 185
Characteristics of the Phase 188
Periodic Nature of the DFT 194
Compression and Expansion, Multirate methods 200
Multiplying Signals (Amplitude Modulation) 204
The Discrete Time Fourier Transform 206
Parseval's Relation 208
Chapter 11. Fourier Transform Pairs
Delta Function Pairs 209
The Sinc Function 212
Other Transform Pairs 215
Gibbs Effect 218
Harmonics 220
Chirp Signals 222
Chapter 12. The Fast Fourier Transform
Real DFT Using the Complex DFT 225
How the FFT Works 228
FFT Programs 233
Speed and Precision Comparisons 237
Further Speed Increases 238
Chapter 13. Continuous Signal Processing
The Delta Function 243
Convolution 246
The Fourier Transform 252
The Fourier Series 255
DIGITAL FILTERS
Chapter 14. Introduction to Digital Filters
Filter Basics 261
How Information is Represented in Signals 265
Time Domain Parameters 266
Frequency Domain Parameters 268
High-Pass, Band-Pass and Band-Reject Filters 271
Filter Classification 274
Chapter 15. Moving Average Filters
Implementation by Convolution 277
Noise Reduction vs. Step Response 278
Frequency Response 280
Relatives of the Moving Average Filter 280
Recursive Implementation 282
Chapter 16. Windowed-Sinc Filters
Strategy of the Windowed-Sinc 285
Designing the Filter 288
Examples of Windowed-Sinc Filters 292
Pushing it to the Limit 293
Chapter 17. Custom Filters
Arbitrary Frequency Response 297
Deconvolution 300
Optimal Filters 307
Chapter 18. FFT Convolution
The Overlap-Add Method 311
FFT Convolution 312
Speed Improvements 316
Chapter 19. Recursive Filters
The Recursive Method 319
Single Pole Recursive Filters 322
Narrow-band Filters 326
Phase Response 328
Using Integers 332
Chapter 20. Chebyshev Filters
The Chebyshev and Butterworth Responses 333
Designing the Filter 334
Step Response Overshoot 338
Stability 339
Chapter 21. Filter Comparison
Match #1: Analog vs. Digital Filters 343
Match #2: Windowed-Sinc vs. Chebyshev 346
Match #3: Moving Average vs. Single Pole 348
APPLICATIONS
Chapter 22. Audio Processing
Human Hearing 351
Timbre 355
Sound Quality vs. Data Rate 358
High Fidelity Audio 359
Companding 362
Speech Synthesis and Recognition 364
Nonlinear Audio Processing 368
Chapter 23. Image Formation and Display
Digital Image Structure 373
Cameras and Eyes 376
Television Video Signals 384
Other Image Acquisition and Display 386
Brightness and Contrast Adjustments 387
Grayscale Transforms 390
Warping 394
Chapter 24. Linear Image Processing
Convolution 397
3×3 Edge Modification 402
Convolution by Separability 404
Example of a Large PSF: Illumination Flattening 407
Fourier Image Analysis 410
FFT Convolution 416
A Closer Look at Image Convolution 418
Chapter 25. Special Imaging Techniques
Spatial Resolution 423
Sample Spacing and Sampling Aperture 430
Signal-to-Noise Ratio 432
Morphological Image Processing 436
Computed Tomography 442
Chapter 26. Neural Networks (and more!)
Target Detection 451
Neural Network Architecture 458
Why Does it Work? 463
Training the Neural Network 465
Evaluating the Results 473
Recursive Filter Design 476
Chapter 27. Data Compression
Data Compression Strategies 481
Run-Length Encoding 483
Huffman Encoding 484
Delta Encoding 486
LZW Compression 488
JPEG (Transform Compression) 494
MPEG 501
Chapter 28. Digital Signal Processors
How DSPs are different 503
Circular Buffering 506
Architecture of the Digital Signal Processor 509
Fixed versus Floating Point 514
C versus Assembly 520
How Fast are DSPs? 526
The Digital Signal Processor Market 531
Chapter 29. Getting Started with DSPs
The ADSP-2106x family 535
The SHARC EZ-KIT Lite 537
Design Example: An FIR Audio Filter 538
Analog Measurements on a DSP System 542
Another Look at Fixed versus Floating Point 544
Advanced Software Tools 546
COMPLEX TECHNIQUES
Chapter 30. Complex Numbers
The Complex Number System 551
Polar Notation 555
Using Complex Numbers by Substitution 557
Complex Representation of Sinusoids 559
Complex Representation of Systems 561
Electrical Circuit Analysis 563
Chapter 31. The Complex Fourier Transform
The Real DFT 567
Mathematical Equivalence 569
The Complex DFT 570
The Family of Fourier Transforms 575
Why the Complex Fourier Transform is Used 577
Chapter 32. The Laplace Transform
The Nature of the s-Domain 581
Strategy of the Laplace Transform 588
Analysis of Electric Circuits 592
The Importance of Poles and Zeros 597
Filter Design in the s-Domain 600
Chapter 33. The z-Transform
The Nature of the z-Domain 605
Analysis of Recursive Systems 610
Cascade and Parallel Stages 616
Spectral Inversion 619
Gain Changes 621
Chebyshev-Butterworth Filter Design 623
The Best and Worst of DSP 630
Glossary
Index |
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