## The Fast Fourier Transform and Its ApplicationsThe Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field. |

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### Contents

FOURIER TRANSFORM PROPERTIES | 30 |

CONVOLUTION AND CORRELATION | 50 |

FOURIER SERIES AND SAMPLED WAVEFORMS | 74 |

Copyright | |

11 other sections not shown

### Common terms and phrases

Acoust aliasing amplitude analysis antenna application array band-pass filter band-pass signal bandwidth cepstrum complex compute the FFT continuous Fourier transform convolution integral convolution theorem convolved defined determined digital filter discrete convolution discrete Fourier transform discrete transform domain Equation evaluate Example Fast Fourier Transform FFT algorithm FFT band-pass filter FFT convolution FFT filter FFT results Figure filter bank filter design Fourier integral Fourier series Fourier trans Fourier transform pair frequency function frequency-domain function h(t function illustrated h(kT Hence IEEE IEEE Trans IEEE Transactions illustrated in Fig imaginary impulse functions impulse response input inverse Fourier transform multiplication node Note number of samples odd function one-dimensional periodic function procedure quadrature rectangular sample interval sample values sampled function sampled waveform shift shown in Fig Signal Processing sinusoid Spectral Speech and Signal Speech Signal Process techniques term two-dimensional FFT waveform weighting function x(kT zero