Random modulation

In modulation theory and stochastic processes theory, Random modulation is the Quadrature modulation of two stochastic baseband signals $x_{c}(t)$ and $x_{s}(t)$ on a carrier frequency $f_{0}$ to form the signal $x(t)$:

$x(t)=x_{c}(t)\cos(2\pi f_{0}t)-x_{s}(t)\sin(2\pi f_{0}t)=\Re \left\{{\underline {x}}(t)e^{j2\pi f_{0}t}\right\}$

where ${\underline {x}}(t)$ is the equivalent baseband representation of the modulated signal $x(t)$

${\underline {x}}(t)=x_{c}(t)+jx_{s}(t)$

Bibliography

• Papoulis, Athanasios; Pillai, S. Unnikrishna (2002). "Random walks and other applications". Probability, random variables and stochastic processes (4th ed.). McGraw-Hill Higher Education. pp. 463–473.
• Template:ItScarano, Gaetano (2009). Segnali, Processi Aleatori, Stima. Centro Stampa d'Ateneo.