## Understanding the FFT: A Tutorial on the Algorithm & Software for Laymen, Students, Technicians & Working Engineers |

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### Contents

Fourier Series and the I r | 27 |

The DFT Algorithm | 66 |

Four Fundamental Theorems | 83 |

Copyright | |

6 other sections not shown

### Common terms and phrases

16 data points 16 Point algorithm amplitude apparent average value BASIC BFLY butterflies C/R TO CONTINUE";A chapter coefficients complex numbers cosine components data array DFT program domain data domain function dot product equation example F(SIN FFT routine Figure forward transform Fourier Analysis Fourier series Fourier Transform FREQ F(COS frequency components frequency domain GOSUB GWBASIC harmonic components harmonic number Horner Scheme illustrate iNiad input data integer line 40 matrix multiply negative frequencies number of data Nyquest frequency obtain odd data points orthogonal output array partial DFT perform a DFT phase shift point DFT PRINT HEADING PRINT:PRINT radians reconstruction REM PLOT DATA RETURN rotated scale factor Shifting Theorem simply sine and cosine sine components sine wave sinusoids spectrum square wave stage F stage of computation Stretching Theorem subroutine summation Taylor series triangle wave twiddle factor variable vectors width Xform XT3N zero