## Analytic function models of noise and modulation |

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### Contents

SUMMARY Paee | 2 |

BANDPASS PROCESSES | 10 |

APPENDKB CORRELATION PROIEFtTIES OF COMPLEX STOCHASTIC | 20 |

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### Common terms and phrases

amplitude analytic counterpart analytic functions Analytic Signal analytic time functions appendix auto-correlation function band-pass process Cauchy principal value complex plane complex stochastic process conjugate analytic convolution type correlation and spectral correlation function cross-correlation function Cwz(t defined Definition delta functional denote the space density of z(t depending on context derived deterministic functions deterministic or stochastic Dirac delta distribution distribution theory distributional convolution distributional Fourier transform equa equation B23 equation Bl Equations 29 frequency func function of z(t function z(t functions and stochastic Hence Hilbert transform integral integrodifferential equations IRE Trans jy(t Lemma Let f(z linear time-invariant systems McGraw-Hill Book member function modulated carriers modulation function NOISE AND MODULATION Papoulis ref phasor polar form power spectral density Px(x quadrature form random variable real low-pass real processes real stochastic processes result of equation Rxx(T RzZ(t sense signal and noise single-sideband singular distribution sinusoidal tion upper half-plane weakly stationary zero