This video gives a comprehensive overview of using a frequency-domain analysis technique for evaluating the input-output statistics of a linear time-invariant system with a wide-sense stationary…

This topic considers extending previous topics on calculating the input-output statistics of a linear time-invariant (LTI) system in response to a wide-sense stationary (WSS) process at the input,…

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…

This video presents the formal definition of the power-spectral density (PSD) of a wide-sense stationary (WSS) process, and its inverse relationship, both through discrete-Time Fourier Transform…

This video introduces the frequency-domain description of stationary processes, through the equivalent but conceptually different ideas of stochastic decompositions and Fourier transforms of moments…

This video considers a wider class of nonstationary processes that share some similarities with wide-sense periodic processes. Such nonstationary processes occur in systems where, for example,…

Second-order statistics are fundamental to the definition of wide-sense stationary (WSS) processes, and this video considers the properties that a WSS autocorrelation sequence (ACS) must satisfy.…

This video starts by considering the common types and definitions of stationary processes used in time-series analysis. This topic then considers meanings and relationships of order-N, strict-sense…

This video discusses some fundamental types of stochastic processes, including predictable processes, unpredictable processes, independent and independent and identically distributed processes,…

As with random vectors, other than in certain special cases, it can be difficult to describe and manipulate random processes through the use of joint-probability density functions (pdfs), although…

This video builds on the Statistical Descriptors introduced in Topic 35 by discussing the covariance matrix, the correlation coefficient, and then the cross-correlation and cross-covariance…