## 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. Providing a concise introduction to the theory and practice of Fourier transforms, this book is invaluable to students of physics, electrical and electronic engineering, and computer science. After a brief description of the basic ideas and theorems, the power of the technique is illustrated through 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 Axial Tomography (CAT scanning). The book concludes by discussing digital methods, with particular attention to the Fast Fourier Transform and its implementation. This new edition has been revised to include new and interesting material, such as convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert–Zernike theorem, Babinet's principle and dipole arrays. |

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### Conteúdo

Physics and Fourier transforms | 1 |

Useful properties and theorems | 20 |

Fraunhofer diffraction | 40 |

signal analysis and communication theory | 66 |

interference spectroscopy and spectral line | 86 |

Twodimensional Fourier transforms | 97 |

Multidimensional Fourier transforms | 105 |

The formal complex Fourier transform | 120 |

Discrete and digital Fourier transforms | 127 |

Appendix | 137 |

143 | |

### Termos e frases comuns

Airy disc amplitude analytic angle antisymmetrical aperture function array autocorrelation axis beam Bessel functions Chapter coefficients coherence complex conjugate convolution theorem cosine curve defined described detector diagram diffraction grating diffraction pattern dipole Dirac comb Dirac wall Dirichlet conditions distance dx dy equation example exponential factor fast Fourier transform filter Fourier pair Fourier series Fourier theory Fraunhofer diffraction frequency fringe pattern fringe visibility Gaussian harmonic Heaviside step-function integral interferometer inverse lattice length light Michelson modulation monochromatic multiplied noise obey the Dirichlet optics origin oscillator output path-difference period perpendicular phase physics Pl(c plane practical pulse q-plane radiation sample separated shape signal sinc-function sine sinusoid slit spacing spectral power density spectrometer spectrum line symmetrical top-hat function transmission transmitted two-dimensional Fourier transform variable vector voltage wave train waveform wavefront wavelength width Wiener–Khinchine theorem x,y-plane zero