Overview

The Fourier transform is one of the important mathematical tools in a wide variety of science and engineering fields. Its application - as Fourier analysis or harmonic analysis - provides useful decompositions of signals into fundamental (""primitive"") components, giving shortcuts in the computation of complicated sums and integrals, and often revealing hidden structure in the data. This text develops the basic definitions, properties and applications of Fourier analysis, the emphasis being on techniques for its application to linear systems, although other applications are also considered. The application of Fourier analysis to a wide variety of signals, including discrete time (or parameter), continuous time (or parameter), finite duration, and infinite duration are discussed in the text.

Full Product Details

Author:   Robert M. Gray ,  Joseph W. Goodman
Publisher:   Springer
Imprint:   Springer
Edition:   1995 ed.
Volume:   322
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   1.590kg
ISBN:  

9780792395850

ISBN 10:   0792395859
Pages:   361
Publication Date:   30 June 1995
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Signals and Systems.- 1.1 Waveforms and Sequences.- 1.2 Basic Signal Examples.- 1.3 Random Signals.- 1.4 Systems.- 1.5 Linear Combinations.- 1.6 Shifts.- 1.7 Two-Dimensional Signals.- 1.8 Sampling, Windowing, and Extending.- 1.9 Probability Functions.- 1.10 Problems.- 2 The Fourier Transform.- 2.1 Basic Definitions.- 2.2 Simple Examples.- 2.3 Cousins of the Fourier Transform.- 2.4 Multidimensional Transforms.- 2.5 * The DFT Approximation to the CTFT.- 2.6 The Fast Fourier Transform.- 2.7 * Existence Conditions.- 2.8 Problems.- 3 Fourier Inversion.- 3.1 Inverting the DFT.- 3.2 Discrete Time Fourier Series.- 3.3 Inverting the Infinite Duration DTFT.- 3.4 Inverting the CTFT.- 3.5 Continuous Time Fourier Series.- 3.6 Duality.- 3.7 Summary.- 3.8 * Orthonormal Bases.- 3.9 * Discrete Time Wavelet Transforms.- 3.10 * Two-Dimensional Inversion.- 3.11 Problems.- 4 Basic Properties.- 4.1 Linearity.- 4.2 Shifts.- 4.3 Modulation.- 4.4 Parseval’s Theorem.- 4.5 The Sampling Theorem.- 4.6 The DTFT of a Sampled Signal.- 4.7 * Pulse Amplitude Modulation (PAM).- 4.8 The Stretch Theorem.- 4.9 * Downsampling.- 4.10 * Upsampling.- 4.11 The Derivative and Difference Theorems.- 4.12 Moment Generating.- 4.13 Bandwidth and Pulse Width.- 4.14 Symmetry Properties.- 4.15 Problems.- 5 Generalized Transforms and Functions.- 5.1 Limiting Transforms.- 5.2 Periodic Signals and Fourier Series.- 5.3 Generalized Functions.- 5.4 Fourier Transforms of Generalized Functions.- 5.5 * Derivatives of Delta Functions.- 5.6 * The Generalized Function ?(g(t)).- 5.7 Impulse Trains.- 5.8 Problems.- 6 Convolution and Correlation.- 6.1 Linear Systems and Convolution.- 6.2 Convolution.- 6.3 Examples of Convolution.- 6.4 The Convolution Theorem.- 6.5 Fourier Analysis of Linear Systems.- 6.6 The Integral Theorem.- 6.7Sampling Revisited.- 6.8 Correlation.- 6.9 Parseval’s Theorem Revisited.- 6.10 * Bandwidth and Pulsewidth Revisited.- 6.11 * The Central Limit Theorem.- 6.12 Problems.- 7 Two Dimensional Fourier Analysis.- 7.1 Properties of 2-D Fourier Transforms.- 7.2 Two Dimensional Linear Systems.- 7.3 Reconstruction from Projections.- 7.4 The Inversion Problem.- 7.5 Examples of the Projection-Slice Theorem.- 7.6 Reconstruction.- 7.7 * Two-Dimensional Sampling Theory.- 7.8 Problems.- 8 Memoryless Nonlinearities.- 8.1 Memoryless Nonlinearities.- 8.2 Sinusoidal Inputs.- 8.3 Phase Modulation.- 8.4 Uniform Quantization.- 8.5 Problems.- A Fourier Transform Tables.

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