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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…

This video introduces the important signal processing application of system identification; identifying the system impulse response or transfer function through measurements. The video highlights…

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…

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…

This Topic extends the definition of the power-spectral density in two ways. First, it considers the cross-power spectral density (CPSD) for considering the spectral characteristics of…

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 gives a very brief introduction to the powerful Markov model for random processes. It considers in detail the first-order Markov process, deriving the joint-probability density…

This video starts to wrap up the Chapter on Stochastic processes by looking at joint signal statistics, such as cross-correlation and cross-covariance, uncorrelated pairs of random processes, and…

This Topic introduces the notion of estimating statistical averages from a single realisation of a stochastic process. This concept is most easily developed for estimating first and second…

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,…

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

In this first video of the Statistical Signal Processing part of the PETARS course, the notion of random signals, or stochastic processes is introduced. It is defined as a natural extension to…