Search for tag: "summation"

Mateus Sousa - Recent developments in Fourier interpolation theory

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…

From  Iain Cms 0 likes 19 plays 0  

Diagonal Cubic Hypersurfaces over F_q(t) - Leonhard Hochfilzer

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

From  Iain Cms 0 likes 48 plays 0  

Topic 43: Perfect Sampling, Derivation of Sampling Theorem, and Adequate Sampling (SNADA, Chapter 8)

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…

From  James Hopgood 0 likes 369 plays 0  

Topic 40: The Impulse Train and its Fourier Spectrum (SNADA, Chapter 7)

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…

From  James Hopgood 2 likes 971 plays 0  

Optional Topic 24: Developing the Complex Fourier Series (SNADA, Chapter 5)

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…

From  James Hopgood 0 likes 241 plays 0  

Topic 20: Revision of Trigonometric Fourier Series (SNADA, Chapter 5)

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…

From  James Hopgood 0 likes 421 plays 0  

REF2020: Feng Yuan- Small-x TMDs an overview

REF2020: Feng Yuan- Small-x TMDs an overview

From  Lyndsey Ballantyne 0 likes 21 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…

From  James Hopgood 0 likes 164 plays 0  

Topic 70: Cross-Power and Complex Spectral Densities (PETARS, Chapter 9)

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…

From  James Hopgood 0 likes 231 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 0 likes 415 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 0 likes 430 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),…

From  James Hopgood 0 likes 192 plays 0  

Topic 46: Cramer-Rao Lower Bound (PETARS, Chapter 6)

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…

From  James Hopgood 0 likes 517 plays 0  

Topic 43: Measuring Performance of an Estimator (PETARS, Chapter 6)

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…

From  James Hopgood 0 likes 259 plays 0  

Topic 40: Sum of Independent Random Variables (PETARS, Chapter 5)

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,…

From  James Hopgood 0 likes 295 plays 0  

Introduction to IFP art and design courses

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.

From  Robbie Bushe 0 likes 264 plays 0