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Fourier Transforms : an Introduction for Engineers

Author: Robert M Gray; Joseph W Goodman
Publisher: Boston, MA : Springer US, 1995.
Series: International series in engineering and computer science, 322.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The Fourier transform is one of the most 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. Fourier Transforms: An  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Robert M Gray; Joseph W Goodman
ISBN: 9781461523598 1461523591
OCLC Number: 852790687
Description: 1 online resource (xx, 361 pages).
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 --
6.7 Sampling 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.
Series Title: International series in engineering and computer science, 322.
Responsibility: by Robert M. Gray, Joseph W. Goodman.

Abstract:

Applications of Fourier transforms, often called Fourier analysis or harmonic analysis, provide useful decompositions of signals into fundamental or "primitive" components, provide shortcuts to the  Read more...

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