Search for tag: "summation"

A Young Researchers Symposium in Harmonic Analysis Mateus Sousa, Basque Center for Applied Mathematics 24 June 2022 This recording is in the process of being subtitled. This typically takes around…

Rational Points on Higher Dimensional Varieties Diagonal Cubic Hypersurfaces over F_q(t) Leonhard Hochfilzer (Göttingen University) 27 April 2022

This Topic begins by discussing the mathematical model of perfect sampling, namely multiplying the signal (that is to be sampled) by an impulse train. Using this model, the Topic discusses how to…

This Topic introduces the concept of the impulse train, a sequence of Dirac delta impulses, which can be used to perform regular sampling of a signal. The impulse train is fundamental to Nyquist…

This Topic provides a derivation of the Complex Fourier series, given the Trigonometric Fourier series and the concept of complex phasors. This further topic is there for students interested in…

This Topic gives a revision of Trigonometric Fourier Series. It builds on the motivation for using signal decompositions for analysing signals, and decomposes any finite power periodic signal…

REF2020: Feng Yuan- Small-x TMDs an overview

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 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…

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.…

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),…

In this video, the question of finding the lower bound on the performance of all estimators for a particular probabilistic problem, as a benchmark with which to compare the performance of a given…

In this video, the question of measuring and quantifying the performance of an estimator is discussed. The video focusses on the concepts and definitions of bias and variance of the probability…

This Topic considers further the sum of random variables that was introduced in Topic 33 on auxiliary variables. The case of independent random variables and vectors is considered specifically,…

Senior Teaching Fellow Robbie Bushe gives an overview of the two art and design courses on International Foundation Programme offer vey the Centre for Open Learning.