## Applications of analytic function theory to analysis of single-sideband angle-modulated systems, Volume 5446John Hoyt Painter, Langley Research Center, United States. National Aeronautics and Space Administration Analytic function theory applications to analysis of single-sideband angle modulated systems. |

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### Contents

SUMMARY | 1 |

SINUSOIDAL SINGLESIDEBAND AMPLITUDEPHASE MODULATION | 10 |

GAUSSIAN SINGLESIDEBAND FREQUENCY MODULATION | 25 |

3 other sections not shown

### Common terms and phrases

A(t+r amplitude analytic function analytic signal angle-modulated signal APPENDIX arbitrary number assumed autocorrelation function Band-pass filter band-pass signal bandwidth Bessel function characteristic function classical FM coc 0 coc complex analytic constant defined denotes depending on context deterministic or stochastic double-sideband equations 22 equivalent phase exp(jcoct exp(jwct Figure four signals frequency modulated func function f(t functions and stochastic Gaussian process Hence high-index Hilbert transform I A(t+r)A(t ideal jg(t jy(t limiter-discriminator linear product demodulation mathematical mean-squared value message function modulated carrier power modulated subcarriers modulating sinusoids modulation index noise process noise spectral density nwm)t phase function presence of noise real band-pass real low-pass residual carrier RyX(r signal and noise signal component signal power signal s(t single-sideband angle-modulation sinusoidal modulation Snn(co so(t Spectral relations SSB angle-modulated SSB-FM stationary processes stochastic processes SyX(co theory tion total modulated carrier total power uniformly distributed upper sideband weakly stationary zero zero-mean