## Nonlinear transformations of random processes |

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### Contents

ENVELOPES AND PREENVELOPES | 1 |

CHARACTERISTIC FUNCTION METHOD | 13 |

CORRELATION FUNCTION METHOD | 27 |

Copyright | |

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### Common terms and phrases

amplitude applied assumed Bessel function boundary conditions boundary value problems central limit theorem central moment change of variables Chapter characteristic function characteristic function method closed form coefficients Combine Eqs complex conjugate computed Contour Integrals corre correlation function corresponding covariance function Cross Correlation defined density differential equation differential operator distribution double integral Edgeworth series eigenfunctions eigenvalues Elliptic Integral entire function envelope detector envelope function ergodic error function Euclidean n-space evaluated example expansion expected value exponential function f(xi Fokker-Planck equation Fourier series Fourier transform frequency response frequency spectrum frequency terms fundamental solution Gamma Function Gaussian distributed Gaussian process Green's function Hermite polynomials Hilbert transform However Hughes Aircraft Company hypergeometric hypergeometric function hypergeometric series I.R.E. Trans impulse response Information Theory input process input random process input signal Insert Eq integer integral equation joint characteristic function joint frequency function kernel Laguerre Function Laguerre polynomials Laplace transform law detector linear detector linear filter low pass filter Markov process mathematical Mercer's theorem modulation modulation indices moments noise theory non-Gaussian nonlinear devices nonlinear transformations normally distributed Nyquist intervals obtain orthogonal orthonormal output correlation function output process output signal PGIT piecewise Poisson distributed power law power series pre-envelope pre-envelope function Price's theorem Probability Density Functions Probability Distributions problem process x(t quadratic quadratic functions QUADRATIC TRANSFORMATIONS quantizing quantizing error random process random variables random walk ratic recurrence relation relation result sampling sampling theorem series representation Siegert solution spectral spectral density spectrum square law stationary stationary process statistical statistical independence stochastic process Substitute Eq techniques theorem Transcendental Functions transformations of random trigonometric function w(xi weighting function wide sense stationary Wiener Wiener process Xi(t zero mean