图书简介

Preface; Style; Target Audience; Overview of Structure; In Gratitude; Keypoints; Basic Notions and the Nature of the Fourier Transform: Why Read this Book?; Software and Reproducibility; Notation; Basic Functions; Analysing Signals by Their Components: Approximating Functions by Mathematical Series: Taylor Series; Fourier Series; What is the Fourier Transform, and What Can It Do?; Everyday Use of the Fourier Transform: Transforms and Speech Recognition; Transforms and Image Compression; Human Hearing and a Transform; Light and Frequency; Summary and Further Reading; The Continuous Fourier Transform: Continuous Fourier Transform Basis: Continuous Signals and Their Fourier Transform; Magnitude and Phase; Inverse Fourier Transform; Fourier Transform in Matlab; Fourier Transform Pairs; Properties of the Continuous Fourier Transform: Superposition; Time Shift; Scaling in Time; Parseval’s Theorem (Rayleigh’s Theorem); Symmetry; Differentiation; Uncertainty Principle; Modulation; Processing Signals Using the Fourier Transform: Convolution; Correlation; What is the Importance of Phase?: Phase in Signal Reconstruction; Phase in Shift Invariance; Windowing the FT Data: Basic Windowing; Hanning and Hamming Window Operators; Window Duration; Other Windowing Functions; Filtering The FT Data: Basic Filters and Signal Processing; Bessel Filters; Summary; The Discrete Fourier Transform: The Sampling Theorem: Sampling Signals; Sampling Process in the Frequency Domain; The Discrete Fourier Transform (DFT): Basic DFT; Inverse DFT; Visualising The Discrete Fourier Transform Data; DFT in Matlab; Discrete Fourier Transform Pairs; Properties of The DFT: Basic Considerations; Linearity/ Superposition; Time Shift; Time Scaling; Parseval’s Theorem (Rayleigh’s Theorem); Symmetry; Differentiation; Importance of Phase — DFT; Discrete Data Windowing Functions; Discrete Convolution and Correlation: Discrete Convolution; Discrete Correlation; Digital Filters; Averaging and Differencing Samples; The Fast Fourier Transform (FFT): The Butterfly Operation and Basic Components of the FFT; Decimation in Time; Radix 2 FFT; Computational Time for FFT Compared with DFT; Optimising the FFT; Even Faster FFT Algorithms; Summary; The Two-Dimensional Fourier Transform: 2-D Functions and Images: Image Formation; Human Vision; Sampling Images; Discrete Images; Discrete Image Frequency Components; 2-D Fourier Transform and Its Inverse: D Continuous Fourier Transform, and Separability; 2-D Discrete Fourier Transform; Properties of The 2-D Discrete Fourier Transform: Displaying Images; Rotation; Scaling; Shift Invariance; The Importance of Phase; Computational Cost of 2-D DFT and FFT; Image Processing via the Fourier Transform: Convolution; Computational Considerations of Image Convolution and Template Convolution; Correlation; Filtering; Summary; Variants of the Fourier Transform: Cosine and Sine Transforms, Including The Discrete Cosine Transform (DCT): 1-D Continuous Transforms; 1-D Discrete Cosine and Sine Transforms; -D Discrete Cosine Transform; Walsh–Hadamard Transform: Walsh Transform; Walsh–Hadamard Transform; Hartley Transform; Image Compression Properties of Fourier, DCT, Walsh and Hartley Transforms; Laplace, Mellin and Fourier Mellin: Laplace and Mellin Transforms; Fourier-Mellin Transform; Z Transform; Wavelets: Filter Banks and Signal Analysis; Gabor Wavelets; Summary; Applications of the Fourier Transform: Overview; Fourier Transforms: The Continuous Fourier Transform and Fourier Optics; Magnitude and Phase, and Beamforming; Properties of the Fourier Transform: Superposition and Fingerprint Analysis; Invariance and Image Texture Analysis; Invariance and Image Registration; Differentiation and Image Feature Extraction; Processing Signals Using the Fourier Transform: Convolution Theorem and Ear Biometrics; Deconvolution and Image Enhancement; Speech Recognition and Correlation; The Importance of Phase and Phase Congruency; Filtering and Denoising, and Image Enhancement; Variants of the Fourier Transform, and Coding; Summary; Who and What was Fourier?: Nature and Origins of the Fourier Transform: The Basic Nature and Definitions of the Fourier Transform; On the Development of the Fourier Transform; Baron Jean Baptiste Joseph Fourier; Final Summary; Ready Reference Time: Summary of Fourier Transforms and Their Variants; Summary of Properties of The Continuous Fourier Transform; Continuous Fourier Transform Pairs; Summary of Properties of The Discrete Fourier Transform; Discrete Fourier Transform Pairs; References; Index;

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