## Discrete Fourier Transformation and Its Applications to Power Spectra Estimation |

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### Contents

Problems | 22 |

DISCRETE FOURIER TRANSFORMATION | 31 |

POWER SPECTRA ESTIMATION USING DFT | 93 |

Copyright | |

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### Common terms and phrases

aliasing approximately asymptotic autocorrelation average power spectrum bandlimited bandlimited function bias circular circular convolution circular shift complex Fourier series convolution convolution theorem correlation cosine—tip CRLL dB/oct decreases derivative direct method discrete data window discrete Fourier transform discrete lag window discrete spectral window double precision energy spectrum evaluated FFT algorithms finite energy folding frequency Fortran Fortran IV Fourier series Fourier series coefficients function x(t given in Fig harmonic Hence IDFT impulse indirect integer interval Kaiser window leakage linear m—th main lobe main—lobe width method using DFT N—term sequence obtained optimal discrete spectral Papoulis parameter sets periodic signal plotted power spectra estimation Prob process x(t pulses radix-2 Rav(T rectangular window RERL sampling period Sav(f shift theorem sidelobe level spectral estimates spectrograms stationary process subroutine Sy(f Table B.3 time—limited transform counterpart transform pair variance waveform x(nAt xN_l