Search for tag: "autocorrelation"

Topic 76: Frequency-domain analysis of input-output statistics (PETARS, Chapter 10)

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…

From  James Hopgood on December 2nd, 2020 0 likes 53 plays 0  

Topic 75: Difference Equation Analysis of Input-Output Time-Domain Statistics (PETARS, Chapter 10)

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,…

From  James Hopgood on November 30th, 2020 0 likes 37 plays 0  

Topic 72: Time-Domain Analysis of Response to Random Signals using the System Impulse Response (PETARS, Chapter 10)

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…

From  James Hopgood on November 26th, 2020 0 likes 59 plays 0  

Topic 69: Definition and Properties of the Power-Spectral Density (PETARS, Chapter 9)

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…

From  James Hopgood on November 19th, 2020 0 likes 55 plays 0  

Topic 68: Concept of the Power Spectral Definition and its Origins (PETARS, Chapter 9)

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…

From  James Hopgood on November 18th, 2020 0 likes 70 plays 0  

Topic 64: Wide-sense periodic, wide-sense cyclo-stationary, and quasi-stationary processes (PETARS, Chapter 8)

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,…

From  James Hopgood on November 11th, 2020 0 likes 81 plays 0  

Topic 63: Properties of Autocorrelation sequences for WSS processes (PETARS, Chapter 8)

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.…

From  James Hopgood on November 8th, 2020 0 likes 85 plays 0  

Topic 62: Stationary and WSS processes (PETARS, Chapter 8)

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…

From  James Hopgood on November 8th, 2020 0 likes 79 plays 0  

Topic 61: Important Types of Stochastic Processes (PETARS, Chapter 8)

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

From  James Hopgood on November 4th, 2020 0 likes 75 plays 0  

Topic 60: Statistical Description of Random Processes (PETARS, Chapter 8)

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…

From  James Hopgood on November 3rd, 2020 0 likes 80 plays 0  

Topic 36: Further Statistical Descriptors (PETARS, Chapter 5)

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…

From  James Hopgood on October 14th, 2020 0 likes 96 plays 0