Consider a narrow band signal (laser) that I can modulate digitally with a on/off switch controlled by a digital pseudo random number generator. The resulting signal features a linewidth broadened by an amount given by the timebase of the number generator.
How do I figure out the analytical expression for spectral density of the modulated signal for a more general case below?
"on" and "off" are the only two possible states of a modulator and the transitions between states are Bernoulli process with probability $p$ or even more general a two states Discrete Markov Process with time base $\tau$.
Approximated solutions are sufficient, but exact solutions would be desirable.
The extreme cases of the Bernoulli process have intuitive results:
- $p=0$ the modulator is permanently "on" therefore the spectral density is unchanged
- $p=1$ the modulator switches regularly in a square wave pattern, a side band is generated at the clock frequency.
I have interest on the general case for Bernoulli process with $0<p<1$ or the Discrete Markov Process.