## A Student's Guide to Fourier Transforms: With Applications in Physics and EngineeringFourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science. |

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### Contents

III | 1 |

IV | 2 |

V | 4 |

VI | 8 |

VII | 10 |

VIII | 11 |

X | 18 |

XI | 20 |

XXX | 69 |

XXXII | 70 |

XXXIII | 76 |

XXXIV | 81 |

XXXV | 86 |

XXXVI | 87 |

XXXVII | 89 |

XXXVIII | 90 |

### Other editions - View all

A Student's Guide to Fourier Transforms: With Applications in Physics and ... J. F. James Limited preview - 2011 |

A Student's Guide to Fourier Transforms: With Applications in Physics and ... J. F. James No preview available - 2002 |

A Student's Guide to Fourier Transforms: With Applications in Physics and ... J. F. James No preview available - 2011 |

### Common terms and phrases

5-function Airy disc amplitude angle antisymmetric aperture function apodising array atoms autocorrelation axis Bessel functions calculation carrier Chapter coefficients coherence complex conjugate constant convolution theorem cosines curve defined described detector diagram diffraction grating dipole Dirac comb Dirac wall Dirichlet conditions distance electrical equation example exponential factor filter finite Fourier pair Fourier series Fourier theory Fraunhofer diffraction frequency fringes Gaussian give GOTO graph grating harmonics Heaviside Heaviside step function infinite input integral intensity interferogram interferometer interval J—oc J—oo lattice Lorentz mathematics modulation monochromatic multiplied optical origin oscillator output parallel Parseval's theorem path-difference period perpendicular phase physics plane practice pulse radiation ratio sampling separated shape signal sinc-function sinusoid slits space spectral power density spectrometer spectrum line symmetrical top-hat function transmission transmitted two-dimensional Fourier transform usually variable vector voltage wave waveform wavefront wavelength width Wiener-Khinchine theorem write zero