Research Catalog

Title

A student's guide to Fourier transforms : with applications in physics and engineering / J.F. James.

Author

James, J. F. (John Francis)

Publication

Cambridge ; New York : Cambridge University Press, 1995.

Items in the Library & Off-site

Holdings

Details

Description

x, 131 pages : illustrations; 24 cm

Subjects

• Fourier transformations
• Mathematical physics
• Engineering mathematics

Bibliography (note)

• Includes bibliographical references (p. 127-128) and index.

Contents

• 1. Physics and Fourier transforms. 1.1. The qualitative approach. 1.2. Fourier series. 1.3. The amplitudes of the harmonics. 1.4. Fourier transforms. 1.5. Conjugate variables. 1.6. Graphical representations -- 2. Useful properties and theorems. 2.1. The Dirichlet conditions. 2.2. Theorems. 2.3. Convolutions and the Convolution Theorem. 2.4. The algebra of convolutions. 2.5. Other theorems. 2.6. Aliasing -- 3. Applications 1: Fraunhofer diffraction. 3.1. Fraunhofer diffraction. 3.3. Polar diagrams. 3.4. Phase and coherence -- 4. Applications 2 : Signal analysis and communication theory. 4.1. Communication channels. 4.2. Noise. 4.3. Filters. 4.4. The Matched Filter Theorem. 4.5. Modulations. 4.6. Multiplex transmission along a channel. 4.7. The passage of some signals through simple filters. 4.8. The Gibbs Phenomenon -- 5. Applications 3: Spectroscopy and spectral line shapes. 5.1. Interference spectrometry. 5.2. The shapes of spectrum lines -- 6. Two-dimensional Fourier transforms.
• 6.1. Cartesian coordinates. 6.2. Polar coordinates. 6.3. Theorems. 6.4. Transforms with circular symmetry. 6.5. Applications. 6.6. Solutions without circular symmetry -- 7. Multi-dimensional Fourier transforms. 7.1. The Dirac wall. 7.2. A 'spike' or 'nail'. 7.3. The Dirac fence. 7.4. The 'bed of nails' -- 8. The formal complex Fourier transform -- 9. Discrete and digital Fourier transforms. 9.1. History. 9.2. The discrete Fourier transform. 9.3. The matrix form of the DFT. 9.4. The BASIC FFT routine.

ISBN

• 0521462983
• 0521468299 (pbk.)

LCCN

94022453

OCLC

• 30783426
• ocm30783426

Owning Institutions

Columbia University Libraries