This video looks at the method for calculating the output statistics for
a linear time-invariant (LTI) system in response to a wide-sense
stationary (WSS) input using a time-domain method given the system
impulse response. The Topic begins by highlighting the conceptual idea
that the expectation of a linear operator or system is equivalent to the
linear operator applied to expectations. This leads to the general idea
that the output statistics are the convolution of the impulse response
of the system with the input statistics. The specific details are
presented, including calculating the mean at the output, the
output-input cross-correlation, the output auto-correlation, and the
equivalent covariance results. A detailed and typical example is
presented, demonstrating the different stages of the calculations.
Finally, the relationship of these results to the application of
stochastic signal modelling is mentioned, and this will be addressed in
detail in a later topic.
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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