## Fourier Transformation for PedestriansMeant to serve an "entertaining textbook," this book belongs to a rare genre. It is written for all students and practitioners who deal with Fourier transformation. Fourier series as well as continuous and discrete Fourier transformation are covered, and particular emphasis is placed on window functions. Many illustrations and easy-to-solve exercises make the book especially accessible, and its humorous style will add to the pleasure of learning from it. |

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### Contents

Introduction | 1 |

Continuous Fourier Transformation | 33 |

Window Functions 69 | 68 |

Discrete Fourier Transformation | 89 |

Filter Effect in Digital Data Processing | 131 |

Solutions | 149 |

197 | |

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### Common terms and phrases

algorithm amplitude asymptotic behaviour autocorrelation average axis basis functions Blackman–Harris window central peak coefﬁcients complex continuous Fourier transformation Convolution Theorem cos(w cos2 cosine cross correlation dB-bandwidth derivative Dirichlet’s discrete Fourier transformation equation example exponential function factor ﬁlter ﬁrst fk+1 forward transformation Fourier series frequency domain function f(t FWHM Gaussian Hence high-pass filter imaginary integral interval inverse transformation Kaiser–Bessel window kink linear Lorentzian low-pass mirroring normal Fourier transformation normalised Nyquist frequency oscillations output Parseval’s theorem partial sum periodic continuation phase shift power representation prefactor pulse QNyq QNyqt r r r r rectangular function rectangular window resolution function Second Shifting Rule Shifting Rule shown in Fig sidelobe suppression signal sin2 sine sinxx spectral components squared there’s transfer function triangular function truncation undershoots unilateral exponential function window functions zeros