This Topic introduces the concept of calculating the stochastic process
at the output of a known deterministic system, given a stochastic
process at the input of the system. This concept is approached by
considering the operation of the system on each realisation of the input
stochastic process, and calculating the statistics over the resulting
ensemble at the output. The video discusses why it is necessary, in this
course, to restrict the analysis to known linear time-invariant (LTI)
systems with wide-sense stationary (WSS) inputs. An overview is provided
for the four different methods for calculating the input-output
statistics, namely in the time-domain or frequency-domain, and either
using the system impulse-response or the system-difference equation.
Finally, an example of simulating the ensemble statistics through a
Monte Carlo experiment is shown.
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
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