## A new twist to Fourier transformsMaking use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership. The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs. |

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### Contents

The Fourier Transform and the Helix | 1 |

Fourier Transforms | 23 |

Continuous Finite and Discrete Fourier Transforms | 65 |

Copyright | |

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100 sample filter 11th bins 40 dB smaller amplitude antenna Artech House beamwidth Cartesian centre Chapter characteristic function Chebyshev complex conjugate convention convolution Cosine wave curve dB or 40 decibels discrete Fourier transform echo signals Equation exponential filter characteristic finite impulse response Fourier series frequency is varied helical waveform helix input integration inverse Fourier transform inverse transform kurtosis lowpass filter major signal frequency Massachusetts Meikle minor signal Modern Radar Systems modulation Multiplication negative phase sequence Norwood output parameters phase sequence component plotted polyphase probability distribution function processing gain Rayleigh distribution rectangular pulse root mean square rotating sampling frequency sampling on spectral Scalloping loss Section 5.1 shown in Figure sidelobe sidelobe level sinc function skew Source spatial spiral spectral leakage spectrum standard deviation statistics Swerling Table tapering functions Truncated Gaussian tapering two-tone characteristics values variable variance vector voltage waveform width Worst case loss zero