## 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

Groundwork | 6 |

Cosine and sine transforms | 17 |

Convolution | 24 |

Copyright | |

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Abel transform abscissa amplitude antenna applied autocorrelation function autocorrelation width band-limited behavior calculate central ordinate Chapter circuit coefficients complex components consider convergence convolution theorem cosine defined derivative differential digits discontinuities discrete discrete Fourier transform domain electrical energy equal equation equivalent width example exponential expression factor filter finite follows formula Fourier series Fourier transform 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 origin output particularly well-behaved function periodic function phase physical plane power spectrum problem pulse quantity rectangle function resistor result sequence serial product shift theorem Show shown in Fig signal sine sine2 smoothing spectra Table theory tion transform pairs two-dimensional unit unity values variable Vi(t voltage waveform zero