## The Fourier transform and its applicationsGroundwork. Convolution. Notation for some useful functions. The impulse symbol. The basic theorems. Doing transforms. The two domains. Electrical waveforms, spectra, and filters. Sampling and series. The laplace transform. Relatives of the fourier transform. Antennas. Television image formation. Convolution in statistics. Noise waveforms. Heat conduction and diffusion. The discrete fourier transform. The discrete hartley transform. The fast hartley transform. Pictorial dictionary of fourier transforms. Supplementary problems. Tables. |

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### Contents

Transforms in the limit | 11 |

Convolution | 24 |

The autocorrelation function | 40 |

Copyright | |

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### Common terms and phrases

Abel transform abscissa amplitude antenna applied autocorrelation function autocorrelation width band-limited function behavior calculate Chapter circuit coefficients complex components consider convergence convolution theorem cosine defined derivative differential equation discontinuity discrete discrete Fourier transform electrical energy equal equivalent width example exponential expression factor filter finite follows formula Fourier series Fourier transform frequency function f(x Gaussian given Hankel transform harmonic Hence Hilbert transform III(x imaginary impulse response impulse symbol infinite input interpolation interval inverse Laplace transform limit linear Mellin transform multiplication notation odd function origin output periodic function phase physical plane power spectrum problem pulse quantity rectangle function result sampling theorem sequence serial product shift theorem Show shown in Fig signal sinc2 sine sine2 spectra Table theory tion transform pairs two-dimensional unity values variable Vi(t voltage Vt(t waveform zero