## Analytic Function Models of Noise and Modulation |

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### Contents

SUMMARY | 1 |

BANDPASS PROCESSES | 10 |

APPENDIX B CORRELATION PROPERTIES OF COMPLEX STOCHASTIC | 20 |

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### Common terms and phrases

amplitude analytic function analytic time functions APPENDIX auto-correlation function band-pass process Cauchy principal value Cauchy-Riemann conditions complex plane complex stochastic process COMPLEX TIME FUNCTIONS conjugate analytic contour correlation and spectral correlation function cross-correlation function Cwz(t 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 B27 equation B3 equations 17 Equations 29 evaluation frequency function of z(t functions and stochastic Hilbert transform integral jv(t jz(t Lemma line integral linear time-invariant systems modulated carriers NOISE AND MODULATION noise function deterministic Papoulis ref phasor polar form power spectral density properties Px(x quadrature form random variable real low-pass real processes real stochastic processes result of equation Rwz(t Rxx(r Rxx(T Rxy(T RyX(T Ryy(T RzX(t RzZ(t signal and noise singular distribution sinusoidal SZZM testing functions 0(t tion upper half-plane weakly stationary