[教材书籍] [下载]傅里叶变换及应用的经典之作The Fourier Transform and Its Applications [推广有奖]

Ronald N. Bracewell 关于傅里叶变换的经典之作The Fourier Transform and Its Applications, the 3rd edition
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格式：djvu
页数：616
目录：
1 Introduction

2 Groundwork
The Fourier Transform and Fourier's Integral Theorem
Conditions for the Existence of Fourier Transforms
Transforms in the Limit
Oddness and Evenness
Significance of Oddness and Evenness
Complex Conjugates
Cosine and Sine Transforms
Interpretation of the Formulas

3 Convolution
Examples of Convolution
Serial Products
Inversion of serial multiplication / The serial product in matrix notation /
Sequences as vectors
Convolution by Computer
The Autocorrelation Function and Pentagram Notation
The Triple Correlation
The Cross Correlation
The Energy Spectrum
4 Notation for Some Useful Functions
Rectangle Function of Unit Height and Base, II(x)
Triangle Function of Unit Height and Area, A(x)
Various Exponentials and Gaussian and Rayleigh Curves
Heaviside's Unit Step Function, H(x)
The Sign Function, sgn x
The Filtering or Interpolating Function, sinc x
Pictorial Representation
Summary of Special Symbols

5 The Impulse Symbol 74
The Sifting Property 78
The Sampling or Replicating Symbol III(x) 81
The Even and Odd Impulse Pairs (x) and Ii(x) 84
Derivatives of the Impulse Symbol 85
Null Functions 87
Some Functions in Two or More Dimensions 89
The Concept of Generalized Function 92

6 The Basic Theorems
A Few Transforms for Illustration
Similarity Theorem
Addition Theorem
Shift Theorem
Modulation Theorem
Convolution Theorem
Rayleigh's Theorem
Power Theorem
Autocorrelation Theorem
Derivative Theorem
Derivative of a Convolution Integral
The Transform of a Generalized Function
Proofs of Theorems
Similarity and shift theorems / Derivative theorem / Power theorem
Summary of Theorems

7 Obtaining Transforms
Integration in Closed Form
Numerical Fourier Transformation
The Slow Fourier Transform Program
Generation of Transforms by Theorems
Application of the Derivative Theorem to Segmented Functions
Measurement of Spectra
Radiofrequency spectral analysis / Optical Fourier transform spectroscopy

8 The Two Domains
Definite Integral
The First Moment
Centroid
Moment of Inertia (Second Moment)
Moments
Mean-Square Abscissa
Radius of Gyration
Contents xi
Variance
Smoothness and Compactness
Smoothness under Convolution
Asymptotic Behavior
Equivalent Width
Autocorrelation Width
Mean Square Widths
Sampling and Replication Commute
Some Inequalities
Upper limits to ordinate and slope / Schwarz's inequality
The Uncertainty Relation
Proof of uncertainty relation / Example of uncertainty relation
The Finite Difference
Running Means
Central Limit Theorem
Summary of Correspondences in the Two Domains

9 Waveforms, Spectra, Filters, and Linearity
Electrical Waveforms and Spectra
Filters
Generality of Linear Filter Theory
Digital Filtering
Interpretation of Theorems
Similarity theorem / Addition theorem / Shift theorem / Modulation theorem /
Converse of modulation theorem
Linearity and Time Invariance
Periodicity

10 Sampling and Series
Sampling Theorem
Interpolation
Rectangular Filtering in Frequency Domain
Smoothing by Running Means
Undersampling
Ordinate and glope Sampling
Interlaced Sampling
Sampling in the Presence of Noise
Fourier Series
Gibbs phenomenon / Finite Fourier transforms / Fourier coefficients
Impulse Trains That Are Periodic
The Shah Symbol Is Its Own Fourier Transform

11 The Discrete Fourier Transform and the FFT
The Discrete Transform Formula
Cyclic Convolution
Examples of Discrete Fourier Transforms
Reciprocal Property
Oddness and Evenness
Examples with Special Symmetry
Complex Conjugates
Reversal Property
Addition Theorem
Shift Theorem
Convolution Theorem
Product Theorem
Cross-Correlation
Autocorrelation
Sum of Sequence
First Value
Generalized Parseval-Rayleigh Theorem
Packing Theorem
Similarity Theorem
Examples Using MATLAB
The Fast Fourier Transform
Practical Considerations
Is the Discrete Fourier Transform Correct?
Applications of the FFT
Timing Diagrams
When N Is Not a Power of 2
Two-Dimensional Data
Power Spectra

12 The Discrete Hartley Transform
A Strictly Reciprocal Real Transform
Notation and Example
The Discrete Hartley Transform
Examples of DHT
Discussion
A Convolution of Algorithm in One and Two Dimensions
Two Dimensions
The Cas-Cas Transform
Theorems
The Discrete Sine and Cosine transforms
Boundary value problems / Data compression application
Computing
Getting a Feel for Numerical Transforms
The Complex Hartley Transform
Physical Aspect of the Hartley Transformation
The Fast Hartley Transform
The Fast Algorithm
Running Time
Timing via the Stripe Diagram
Matrix Formulation
Convolution
Permutation
A Fast Hartley Subroutine

13 Relatives of the Fourier Transform
The Two-Dimensional Fourier Transform
Two-Dimensional Convolution
The Hankel Transform
Fourier Kernels
The Three-Dimensional Fourier Transform
The Hankel Transform in n Dimensions
The Mellin Transform
The z Transform
The Abel Transform
The Radon Transform and Tomography
The Abel-Fourier-Hankel ring of transforms / Projection-slice theorem /
Reconstruction by modified back projection
The Hilbert Transform
The analytic signal / Instantaneous frequency and envelope / Causality
Computing the Hilbert Transform
The Fractional Fourier Transform
Shift theorem / Derivative theorems / Fractional convolution theorem /
Examples of transforms

14 The Laplace Transform
Convergence of the Laplace Integral
Theorems for the Laplace Transform
Transient-Response Problems
Laplace Transform Pairs
Natural Behavior
Impulse Response and Transfer Function
Initial-Value Problems
Setting Out Initial-Value Problems
Switching Problems

15 Antennas and Optics
One-Dimensional Apertures
Analogy with Waveforms and Spectra
Beam Width and Aperture Width
Beam Swinging
Arrays of Arrays
Interferometers
Spectral Sensitivity Function
Modulation Transfer Function
Physical Aspects of the Angular Spectrum
Two-Dimensional Theory
Optical Diffraction
Fresnel Diffraction
Other Applications of Fourier Analysis

16 Applications in Statistics
Distribution of a Sum
Consequences of the Convolution Relation
The Characteristic Function
The Truncated Exponential Distribution
The Poisson Distribution

17 Random Waveforms and Noise
Discrete Representation by Random Digits
Filtering a Random Input: Effect on Amplitude Distribution
Digression on independence / The convolution relation
Effect on Autocorrelation
Effect on Spectrum
Spectrum of random input / The output spectrum
Some Noise Records
Envelope of Bandpass Noise
Detection of a Noise Waveform
Measurement of Noise Power

18 Heat Conduction and Diffusion
One-Dimensional Diffusion
Gaussian Diffusion from a Point
Diffusion of a Spatial Sinusoid
Sinusoidal Time Variation

19 Dynamic Power Spectra
The Concept of Dynamic Spectrum
The Dynamic Spectrograph
Computing the Dynamic Power Spectrum
Frequency division / Time division / Presentation
Equivalence Theorem
Envelope and Phase
Using log f instead of f
The Wavelet Transform
Adaptive Ceil Placement
Elementary Chirp Signals (Chirplets)
The Wigner Distribution

20 Tables of sinc x, sinc 2 x, and exp (--'J'/'X 2)

21 Solutions to Selected Problems
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19

22 Pictorial Dictionary of Fourier Transforms
Hartley Transforms of Some Functions without Symmetry

23 The Life of Joseph Fourier
Index