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E-grāmata: Sinusoids: Theory and Technological Applications

(University of New Orleans, Louisiana, USA)
  • Formāts: 519 pages
  • Izdošanas datums: 08-Jul-2014
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781040071052
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Sinusoids: Theory and Technological ApplicationsPalielināt
  • Formāts: 519 pages
  • Izdošanas datums: 08-Jul-2014
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781040071052
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A Complete Treatment of Current Research Topics in Fourier Transforms and Sinusoids





Sinusoids: Theory and Technological Applications explains how sinusoids and Fourier transforms are used in a variety of application areas, including signal processing, GPS, optics, x-ray crystallography, radioastronomy, poetry and music as sound waves, and the medical sciences. With more than 200 illustrations, the book discusses electromagnetic force and sychrotron radiation comprising all kinds of waves, including gamma rays, x-rays, UV rays, visible light rays, infrared, microwaves, and radio waves. It also covers topics of common interest, such as quasars, pulsars, the Big Bang theory, Olbers paradox, black holes, Mars mission, and SETI.





The book begins by describing sinusoidswhich are periodic sine or cosine functionsusing well-known examples from wave theory, including traveling and standing waves, continuous musical rhythms, and the human liver. It next discusses the Fourier series and transform in both continuous and discrete cases and analyzes the Dirichlet kernel and Gibbs phenomenon. The author shows how invertibility and periodicity of Fourier transforms are used in the development of signals and filters, addresses the general concept of communication systems, and explains the functioning of a GPS receiver. The author then covers the theory of Fourier optics, synchrotron light and x-ray diffraction, the mathematics of radioastronomy, and mathematical structures in poetry and music. The book concludes with a focus on tomography, exploring different types of procedures and modern advances. The appendices make the book as self-contained as possible.

Recenzijas

"... I highly recommend this book as a good source for individual studies for graduate students, scientists and technical experts." --Krzysztof Stempak (Wroclaw), Zentralblatt MATH 1306 | 1

Preface xv
Notations, Definitions, and Acronyms xix
1 Introduction
1(30)
1.1 Definitions
1(2)
1.2 Continuous Sinusoids
3(6)
1.3 Discrete Sinusoids
9(1)
1.4 Harmonic Series
10(1)
1.5 Traveling and Standing Waves
10(9)
1.5.1 Vibrating String
15(4)
1.6 Wave Propagation and Dispersion
19(6)
1.6.1 Heat Waves
24(1)
1.7 Applications of Sinusoids
25(1)
1.8 Historical Notes
26(5)
2 Fourier Series
31(26)
2.1 Orthogonality
31(4)
2.2 Completeness and Uniform Convergence
35(1)
2.3 Fourier Series
36(6)
2.3.1 Some Special Cases
38(1)
2.3.2 Amplitude and Phase Form
38(2)
2.3.3 Fourier Sine Series
40(1)
2.3.4 Fourier Cosine Series
41(1)
2.3.5 Uniform Convergence
41(1)
2.4 Dirac Delta Function
42(3)
2.5 Delta Function and Dirichlet Kernel
45(2)
2.6 Gibbs Phenomenon
47(3)
2.6.1 Sigma-Approximation
48(2)
2.7 Square Waveform
50(2)
2.8 Examples of Fourier Series
52(1)
2.9 Complex Fourier Coefficients
53(4)
3 Fourier Transforms
57(40)
3.1 Definitions
57(13)
3.1.1 Fourier Integral
59(1)
3.1.2 Properties of Fourier Transforms
59(1)
3.1.3 Fourier Transforms of the Derivatives of a Function
60(1)
3.1.4 Convolution Theorems for Fourier Transform
61(2)
3.1.5 Fourier Transforms of Some Typical Signals
63(4)
3.1.6 Poisson's Summation Formula
67(1)
3.1.7 Sine and Cosine Transforms
68(2)
3.2 Finite Fourier Transforms
70(5)
3.2.1 Properties
72(1)
3.2.2 Finite Fourier Transforms of Derivatives
72(1)
3.2.3 Periodic Extensions
72(1)
3.2.4 Convolution
73(1)
3.2.5 Differentiation with Respect to a Parameter
74(1)
3.3 Fourier Transforms of Two Variables
75(10)
3.3.1 Local Spatial Frequency
75(2)
3.3.2 Fourier Transform of Signals
77(1)
3.3.3 Circle Function
78(1)
3.3.4 Amplitude Transmittance Function
79(1)
3.3.5 Convolution
80(1)
3.3.6 Symmetry of Fourier Transform
81(1)
3.3.7 Image Rotation
81(1)
3.3.8 Other Properties of 2-D Fourier Transform
81(3)
3.3.9 Grating
84(1)
3.4 Fourier Transforms: Discrete Case
85(5)
3.4.1 Discrete Signal
87(3)
3.5 Fast Fourier Transform
90(2)
3.5.1 Radix-2 Algorithm for FFT
91(1)
3.6 Multiple Fourier Transform
92(1)
3.7 Fourier Slice Theorem
93(4)
4 Signals and Filters
97(54)
4.1 Description of Signals
97(3)
4.2 Convolution and Signals
100(3)
4.3 Theory of Signals
103(9)
4.3.1 Types of Signals
103(1)
4.3.2 Continuous Deterministic Signals
104(1)
4.3.3 Discrete Deterministic Signals
104(4)
4.3.4 Bandpass Signals
108(1)
4.3.5 Continuous-Time Domain
109(1)
4.3.6 Linear and Nonlinear Systems
110(1)
4.3.7 Time-Invariant and Time-Varying Systems
110(1)
4.3.8 Causal and Noncausal Systems
110(1)
4.3.9 Linear Time-Invariant Systems
111(1)
4.4 Random Signals
112(8)
4.4.1 Discrete Case
113(1)
4.4.2 Random Sequence of Pulses
113(1)
4.4.3 Sampling
114(1)
4.4.4 Amplitude
115(2)
4.4.5 Frequency
117(1)
4.4.6 Superposition of Signals
118(1)
4.4.7 Periodic Signals
119(1)
4.5 Discrete Fourier Analysis
120(7)
4.5.1 Fourier Series of Elementary Waveforms
123(4)
4.6 Fourier Resynthesis: Discrete Case
127(6)
4.6.1 Additive Synthesis
128(1)
4.6.2 Time and Phase Shifts
129(3)
4.6.3 Nonperiodic Signals
132(1)
4.7 Theory of Filters
133(18)
4.7.1 Delay Network
134(2)
4.7.2 Classification of Filters
136(12)
4.7.3 Properties and Uses
148(3)
5 Communication Systems
151(30)
5.1 Communication Channels
151(1)
5.2 Noise
152(2)
5.3 Quantization
154(5)
5.4 Digital Signals
159(2)
5.4.1 Amplitude and Phase Characteristic
160(1)
5.5 Interference
161(4)
5.5.1 Light Sources
163(1)
5.5.2 Laser Beam
163(1)
5.5.3 Astronomical Interferometry
163(1)
5.5.4 Acoustic Interferometry
164(1)
5.5.5 Quantum Interference
164(1)
5.6 Nonlinear Systems
165(1)
5.7 SDR System
165(2)
5.8 Data Transmission
167(1)
5.9 Space Exploration
168(6)
5.9.1 Error-Correcting Codes
169(4)
5.9.2 Combustion
173(1)
5.9.3 Combustion Instability
173(1)
5.10 Mars Project and Beyond
174(7)
5.10.1 SETI
179(2)
6 Global Positioning System
181(50)
6.1 GPS Structure
181(14)
6.1.1 Bancroft's Method
182(2)
6.1.2 Trilateration Method
184(3)
6.1.3 GPS Segments
187(5)
6.1.4 Navigation
192(1)
6.1.5 Accuracy
193(1)
6.1.6 Applications
194(1)
6.2 CDMA Principle
195(5)
6.2.1 CDMA Signals
197(1)
6.2.2 Differential GPS (DGPS) Techniques
197(1)
6.2.3 GPS Error Sources
198(2)
6.3 C/A Code Architecture
200(21)
6.3.1 Gold Codes
201(3)
6.3.2 C/A Code and Data Format
204(1)
6.3.3 GPS Signal Waveform: L1 Channel
205(1)
6.3.4 DSSS
205(1)
6.3.5 BPSK
206(1)
6.3.6 GPS Frequency
206(3)
6.3.7 Navigation
209(1)
6.3.8 GPS Signal Structure
209(2)
6.3.9 C/A Code Acquisition
211(1)
6.3.10 Serial Search Algorithm
212(1)
6.3.11 Time Domain Correlation
213(3)
6.3.12 Domain Correlation
216(3)
6.3.13 Delayed Signal
219(2)
6.4 P Code Architecture
221(8)
6.4.1 P Code Acquisition
226(2)
6.4.2 P Code Spectral Density
228(1)
6.5 Computational Aspects
229(2)
7 Fourier Optics
231(36)
7.1 Physical Optics
231(3)
7.1.1 Abbe Sine Condition
233(1)
7.2 Scalar Diffraction Theory
234(20)
7.2.1 Helmholtz Equation
236(1)
7.2.2 Helmholtz-Kirchhoff Integral Theorem
236(3)
7.2.3 Fresnel-Kirchhoff Diffraction
239(1)
7.2.4 Rayleigh-Sommerfeld Diffraction
240(4)
7.2.5 Fresnel Diffraction
244(1)
7.2.6 Huygens-Fresnel Principle
244(1)
7.2.7 Fresnel Approximation
245(6)
7.2.8 Fraunhofer Diffraction
251(3)
7.3 Quasi-Optics
254(5)
7.4 Electromagnetic Spectrum
259(5)
7.5 Electromagnetic Radiation
264(1)
7.6 Adaptive Additive Algorithm
265(2)
8 X-Ray Crystallography
267(30)
8.1 Historical Notes
267(1)
8.2 Bragg's Law
267(3)
8.3 X-Ray Diffraction
270(3)
8.3.1 Electron Distribution
271(2)
8.4 Generation of X-Rays
273(1)
8.5 DNA
274(4)
8.6 Hydrogen Atom
278(8)
8.6.1 Hydrogen Spectrum
283(3)
8.7 Units of Measurement
286(3)
8.7.1 Ultrashort Pulse
288(1)
8.8 Laser
289(8)
8.8.1 Luminescence
293(4)
9 Radioastronomy
297(24)
9.1 Historical Notes
297(1)
9.2 Synchrotron Radiation
298(3)
9.3 Radioastronomy
301(1)
9.4 Radio Interferometry
302(4)
9.5 Aperture Synthesis
306(2)
9.6 Big Bang, Quasars, and Pulsars
308(7)
9.6.1 Quasars
309(3)
9.6.2 Pulsars
312(1)
9.6.3 Olbers Paradox
313(2)
9.7 Black Holes
315(6)
9.7.1 A Mathematical Theory
316(1)
9.7.2 Black Hole Solutions
316(5)
10 Acoustics, Poetry, and Music
321(30)
10.1 Introduction
321(2)
10.2 Harmonic Analysis
323(2)
10.3 Huygens Principle Revisited
325(1)
10.4 Modulation
326(3)
10.4.1 Audio Signals
327(2)
10.5 Rhythm and Music
329(15)
10.5.1 Pitch, Loudness, and Timbre
329(3)
10.5.2 Music Bars
332(3)
10.5.3 Timbre
335(1)
10.5.4 Harmonics
336(4)
10.5.5 Musical Scales
340(1)
10.5.6 Tempered Scale
341(2)
10.5.7 Resonance
343(1)
10.6 Drums
344(5)
10.6.1 Vibrating Rectangular Membrane
346(1)
10.6.2 Frequency Modulation
347(2)
10.7 Music Synthesizers
349(2)
11 Computerized Axial Tomography
351(22)
11.1 Introduction
351(3)
11.2 Types of Tomography
354(9)
11.2.1 Straight-Ray Imaging
354(1)
11.2.2 Series Expansion Method
354(1)
11.2.3 Sinogram
355(1)
11.2.4 B-Scan Imaging
356(3)
11.2.5 Reflection Tomography
359(4)
11.3 Magnetic Resonance Imaging
363(6)
11.3.1 Nonlocality of Radon Inversion
368(1)
11.4 Modern Tomography
369(4)
11.4.1 Nuclear Medicine
371(2)
A Tables of Fourier Transforms
373(4)
A.1 Complex Fourier Transform Pairs
373(2)
A.2 Fourier Cosine Transform Pairs
375(1)
A.3 Fourier Sine Transform Pairs
376(1)
B Hilbert Transforms
377(6)
B.1 Hilbert Transforms
377(2)
B.2 Inverse Hilbert Transforms
379(1)
B.3 Discrete Hilbert Transforms
380(3)
C Radon Transforms
383(14)
C.1 Radon Transform
383(2)
C.2 Inverse Radon Transform
385(2)
C.3 2-D Radon Transform
387(1)
C.4 Discrete Radon Transform
388(9)
C.4.1 DRT and Sinogram
390(1)
C.4.2 Inverse DRT: Continuous Case
391(1)
C.4.3 IDRT as Approximate IFT
392(1)
C.4.4 Relationship with Fourier Transform
393(1)
C.4.5 Tomographic Reconstruction Methods
394(1)
C.4.6 Practical Issues
395(2)
D Maxwell's Equations and Solitons
397(12)
D.1 Maxwell's Equations
397(2)
D.2 Sine-Gordon Equation
399(6)
D.3 K-dV Equation
405(2)
D.4 Nonlinear Schrodinger Equation
407(2)
E Modulation
409(10)
E.1 Definition
409(2)
E.2 Phase Modulation and FM
411(2)
E.3 Waveshaping
413(5)
E.4 BPSK Modulation
418(1)
F Boolean and Bitwise Operations
419(2)
G Galois Field
421(8)
G.1 Galois Field Arithmetic
421(3)
G.2 LFSR Encoder
424(5)
H GPS Geometry
429(6)
H.1 Earth
429(1)
H.2 User Location
430(1)
H.3 Altitude
431(2)
H.4 Sidereal Day
433(1)
H.5 Kepler's Laws
433(2)
I Gold Codes
435(4)
I.1 Definition
435(1)
I.2 m-Sequences
436(2)
I.3 Gold Code Generator
438(1)
J Doppler Effect
439(4)
K Bessel Functions
443(6)
K.1 Bessel functions of the First Kind
443(1)
K.2 Modified Bessel Functions
444(1)
K.3 Airy Functions
445(1)
K.4 Hankel Transforms
445(4)
L Heisenberg's Uncertainty Principle
449(4)
M Classical Latin Prosody
453(10)
M.1 Rhythm and Meter
453(2)
M.2 Feet
455(1)
M.3 List of Feet
456(2)
M.4 Division of Rhythms
458(2)
M.5 Roman Concept of Music and Drama
460(3)
Bibliography 463(16)
Index 479
Prem K. Kythe is a Professor Emeritus of Mathematics at the University of New Orleans. He is the author/coauthor of ten books and author of 46 research papers. His research interests encompass the fields of complex analysis, continuum mechanics, and wave theory, including boundary element methods, finite element methods, conformal mappings, PDEs and boundary value problems, linear integral equations, computation integration, fundamental solutions of differential operators, Greens functions, and coding theory.
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