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THE FOURIER INTEGRAL AND ITS APPLICATIONS2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

THE FOURIER INTEGRAL AND ITS APPLICATIONS
  • ATHANASIOS PAPOULIS 著
  • 出版社： INC.
  • ISBN：
  • 出版时间：1962
  • 标注页数：318页
  • 文件大小：10MB
  • 文件页数：326页
  • 主题词：

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图书目录

PART ONE1

Chapter 1．Introduction1

1-1．Fourier Analysis1

1-2．The Laplace Transform2

1-3．Linear Systems4

1-4．Singularity Functions5

1-5．The Fourier Transform in Probability Theory6

Chapter 2．Basic Theorems and Examples7

2-1．The Fourier Integral7

2-2．Special Forms of the Fourier Integral10

2-3．Simple Theorems14

2-4．Examples18

2-5．The Convolution Theorem25

2-6．On the Proof of the Fourier-integral Theorem29

Chapter 3．Singularity Functions and Line Spectra35

3-1．Basic Examples36

3-2．Fourier Series42

3-3．Poisson＇s Sum Formula47

3-4．Periodic-frequency Spectra49

3-5．Sampling Theorem50

Chapter 4．Numerical Techniques and Uncertainty Principle53

4-1．Evaluation of the Fourier Transform53

4-2．Evaluation of the Inversion Integral56

4-3．Approximate Evaluation ofthe Convolution Integral59

4-4．Duration of a Signal and Uncertainty Principle62

4-5．Generalization of the Uncertainty Principle67

Problems75

Solutions77

PART TWO81

Chapter 5．Linear Systems81

5-1．Definitions81

5-2．The System Function86

5-3．Evaluation of the Step Response89

Chapter 6．Low-pass Filters94

6-1．Definitions94

6-2．Amplitude Distortion97

6-3．Causal Systems with Linear Phase106

6-4．Phase Distortion108

6-5．Summary119

Chapter 7．Bandpass Filters120

7-1．Symmetrical Systems120

7-2．Modulated Input127

7-3．Unsymmetrical Systems131

7-4．Modulated Input133

7-5．Group，Phase，and Signal-front Delay134

7-6．Group，PHase，and Signal-front Velocity136

7-7．The Principle of Stationary Phase139

Chapter 8．Spectrum Analyzers144

8-1．Simultaneous Spectral Analysis145

8-2．Sequential Spectral Analysis150

8-3．Periodic Signals153

Problems161

Solutions165

PART THREE169

Chapter 9．The Laplace Transform169

9-1．The Unilateral Laplace Transform169

9-2．Relationship between the Fourier Integral of a Causal Function and the Unilateral Laplace Transform172

9-3．The Inversion Formula175

9-4．Evaluation of f(t)176

9-5．Initial-value Theorem186

9-6．The Bilateral Laplace Transform187

Chapter 10．Integral Theorems192

10-1．Integral Theorems192

10-2．Relationship between R(ω)and X(ω)195

10-3．Minimum-phase-shift Functinos204

10-4．Energy of a Signal212

10-5．Causality Conditions213

Problems218

Solutions220

PART FOUR223

Chapter 11．Positive Functions and Limit Theorems223

11-1．The Density Function223

11-2．Repeated Convolution226

11-3．The Central-limit Theorem227

11-4．Error Correction233

Chapter 12．Generalized Harmonic Analysis，Correlation，and Power Spectra240

12-1．Introduction240

12-2．Finite Energy Signals241

12-3．Finite Power Signals245

12-4．Functions with Arbitrary Power Spctra254

12-5．Generalized Harmonic Analysis259

Problems265

Solutions266

APPENDIXES269

Appendix Ⅰ．The Impulse Function as Distribution269

Ⅰ-1．Definitions270

Ⅰ-2．Generalized Limits277

Ⅰ-3．Physical Concepts as Distributions281

Appendix Ⅱ．Analytic Functions283

Ⅱ-1．Definitions283

Ⅱ-2．Integration290

Ⅱ-3．Calculus of Residues296

Ⅱ-4．Saddle-point Method of Integration302

Ⅱ-5．Positive Real Functions307

Index313

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