The discrete fourier transform : theory, algorithms and applications / D. Sundararajan.

Format:

Book

Author/Creator:

Sundararajan, D.

Language:

English

Subjects (All):

Fourier transformations.

Mathematical physics.

Physical Description:

xiii, 374 pages : illustrations ; 23 cm

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, [2001]

Summary:

Addressed to senior undergraduate/graduate students in math, engineering, computer science, physics, and other areas studying discrete transforms, this text takes a more practical than abstract approach to discrete Fourier transform theory (widely used for the analysis and design of signals and systems), algorithms, and applications. Includes numerous figures; exercises; appended material on complex numbers, the measure of computational complexity, bit-reversal and prime-factor DFT algorithms, and the testing of programs; mathematical formulas; answers to selected exercises; and a glossary. While the author's e-mail address is given, his professional affiliation is not. c. Book News Inc.

Contents:

1.1 The Transform Method 1

1.2 The Organization of this Book 3

Chapter 2 The Discrete Sinusoid 7

2.1 Signal Representation 7

2.2 The Discrete Sinusoid 11

Chapter 3 The Discrete Fourier Transform 31

3.1 The Fourier Analysis and Synthesis of Waveforms 32

3.2 The DFT and the IDFT 37

3.3 DFT Representation of Some Signals 44

3.4 Direct Computation of the DFT 51

3.5 Advantages of Sinusoidal Representation of Signals 54

Chapter 4 Properties of the DFT 61

4.1 Linearity 61

4.2 Periodicity 62

4.3 Circular Shift of a Time Sequence 62

4.4 Circular Shift of a Spectrum 66

4.5 Time-Reversal Property 69

4.6 Symmetry Properties 71

4.7 Transform of Complex Conjugates 81

4.8 Circular Convolution and Correlation 82

4.9 Sum and Difference of Sequences 85

4.10 Padding the Data with Zeros 86

4.11 Parseval's Theorem 90

Chapter 5 Fundamentals of the PM DFT Algorithms 95

5.1 Vector Format of the DFT 96

5.2 Direct Computation of the DFT with Vectors 101

5.3 Vector Format of the IDFT 104

5.4 The Computation of the IDFT 104

5.5 Fundamentals of the PM DIT DFT Algorithms 106

5.6 Fundamentals of the PM DIF DFT Algorithms 112

5.7 The Classification of the PM DFT Algorithms 114

Chapter 6 The u x 1 PM DFT Algorithms 121

6.1 The u x 1 PM DIT DFT Algorithms 122

6.2 The 2 x 1 PM DIT DFT Algorithm 125

6.3 Reordering of the Input Data 128

6.4 Computation of a Single DFT Coefficient 130

6.5 The u x 1 PM DIF DFT Algorithms 132

6.6 The 2 x 1 PM DIF DFT Algorithm 134

6.7 Computational Complexity of the 2 x 1 PM DFT Algorithms 135

6.8 The 6 x 1 PM DIT DFT Algorithm 138

6.9 Flow Chart Description of the 2 x 1 PM DIT DFT Algorithm 141

Chapter 7 The 2 x 2 PM DFT Algorithms 151

7.1 The 2 x 2 PM DIT DFT Algorithm 151

7.2 The 2 x 2 PM DIF DFT Algorithm 154

7.3 Computational Complexity of the 2 x 2 PM DFT Algorithms 158

Chapter 8 DFT Algorithms for Real Data - I 163

8.1 The Direct Use of an Algorithm for Complex Data 163

8.2 Computation of the DFTs of Two Real Data Sets at a Time 166

8.3 Computation of the DFT of a Single Real Data Set 169

Chapter 9 DFT Algorithms for Real Data - II 175

9.1 The Storage of Data in PM RDFT and RIDFT Algorithms 175

9.2 The 2 x 1 PM DIT RDFT Algorithm 176

9.3 The 2 x 1 PM DIF RIDFT Algorithm 180

9.4 The 2 x 2 PM DIT RDFT Algorithm 187

9.5 The 2 x 2 PM DIF RIDFT Algorithm 190

Chapter 10 Two-Dimensional Discrete Fourier Transform 195

10.1 The 2-D DFT and IDFT 195

10.2 DFT Representation of Some 2-D Signals 196

10.3 Computation of the 2-D DFT 200

10.4 Properties of the 2-D DFT 205

10.5 The 2-D PM DFT Algorithms 212

Chapter 11 Aliasing and Other Effects 225

11.1 Aliasing Effect 226

11.2 Leakage Effect 231

11.3 Picket-Fence Effect 244

Chapter 12 The Continuous-Time Fourier Series 249

12.1 The 1-D Continuous-Time Fourier Series 249

12.2 The 2-D Continuous-Time Fourier Series 262

Chapter 13 The Continuous-Time Fourier Transform 273

13.1 The 1-D Continuous-Time Fourier Transform 273

13.2 The 2-D Continuous-Time Fourier Transform 282

Chapter 14 Convolution and Correlation 287

14.1 The Direct Convolution 287

14.2 The Indirect Convolution 289

14.3 Overlap-Save Method 292

14.4 Two-Dimensional Convolution 295

14.5 Computation of Correlation 298

Chapter 15 Discrete Cosine Transform 303

15.1 Orthogonality Property Revisited 303

15.2 The 1-D Discrete Cosine Transform 305

15.3 The 2-D Discrete Cosine Transform 309

Chapter 16 Discrete Walsh-Hadamard Transform 313

16.1 The Discrete Walsh Transform 313

16.2 The Naturally Ordered Discrete Hadamard Transform 320

16.3 The Sequency Ordered Discrete Hadamard Transform 325

Appendix A The Complex Numbers 333

Appendix B The Measure of Computational Complexity 341

Appendix C The Bit-Reversal Algorithm 343

Appendix D Prime-Factor DFT Algorithm 347

Appendix E Testing of Programs 349.

Notes:

Includes bibliographical references and index.

ISBN:

9810245211

OCLC:

47718203