Shot noise in continuous time

Last time we have moved away from mathematical abstraction of point events by considering pulses of finite duration. Yet the theory we have derived in the earlier post did not fully match the simulated power spectral density. In this post we will see that the discrepancy close to the Nyquist frequency arises due to the observations being made in discrete time.

Shot noise

In the last few posts we have looked at spectral densities of a select point processes. In those posts we have represented events as points on the time axis. Such approach is just an approximation, which is valid when the duration of events is negligible, but it is not always so. When the events have finite duration, but the process is otherwise identical to the Poisson process, we obtain a peculiar type of noise known as the shot noise.