214 pages · 2022
Advanced Probability and Statistics
Remarks and Problems
By Harish Parthasarathy
- Published
- December 22, 2022
- Imprint
- CRC Press
- Edition
- 1st Edition
- ISBN
- 9781003353447
Overview
About this book
The chapters in this book deal with:
Basic formulation of waveguide cavity resonator equations especially when the cross sections of the guides and resonators have arbitrary shapes. The focus is on expressing the total field energy within such a cavity resonator as a quadratic form in the complex coefficients that determine the modal expansions of the electromagnetic field The reviews of basic statistical signal processing covering linear models, fast algorithms for estimating the parameters in such linear models, applications of group representation theory to image processing problems especially the representations of the permutation groups and induced representation theory applied to image processing problems involving the three dimensional Euclidean motion group The Hartree-Fock equations for approximately solving the two electron atomic problem taking spin-orbit magnetic field interactions into account has been discussed. In the limit as the lattice tends to a continuum, the convergence of the stochastic differential equations governing interacting particles on the lattice to a hydrodynamic scaling limit
It will be useful to undergraduate and postgraduate students with courses on transmission lines and waveguides, and statistical signal processing.
Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Subjects
Engineering & Technology, Mathematics & Statistics, Physical Sciences
Inside the book
Table of contents
Select a chapter to read its abstract.
Chapter Chapter 1Remarks and Problems on Transmission Lines and Waveguides
Pages: 18
Study about the historical development of the Maxwell equations for electromagnetism starting with the experimental findings and theoretical formulations of Coulomb, Ampere, Oorsted, Faraday, Gauss and finally culminating in Maxwell’s introduction of the displacement current to satisfy charge conservation in time varying situations. After Newton, the next major unification in physics came with Maxwell when he created the four laws of electromagnetism based on the findings of Coulomb, Gauss, Ampere, Oorsted and Faraday and using these laws predicted that electricity, magnetism and light are one and the same phenomena which appear distinct phenomena to us primarily because of the frequencies at which these propagate. The quality factor of a guide is defined as the ratio of the average energy stored per unit length of the guide to the energy dissipated per unit length per cycle. The cosine term represents the slowly varying envelope of the wave while the cosine term represents the sharp variations of the signal within the envelope.
Chapter Chapter 2Remarks and Problems on Statistical Signal Processing
Pages: 114
[1] Construct the Lattice filter order recursion for an ℝ M -valued vector stationary stochastic process X(t), t ∈ ℤ by minimizing https://www.w3.org/1998/Math/MathML" display="block"> E [ ‖ X ( t ) + ∑ k = 1 p A ( k ) X ( t − k ) 2 ‖ ] https://www.w3.org/1999/xlink" content-type="black-white" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003353447/33d45e82-2e44-4e42-8180-04a739205e5f/content/math2_19_1_B.tif"/> with respect to the M × M prediction coefficient matrices A (k), k = 1, 2, ..., p.
Chapter Chapter 3Some Study Projects on Applied Signal Processing Remarks About Related Contributions of Scientists
Pages: 73
[1] Linear models: Time series models like AR, MA, ARMA, casting these models in the form https://www.w3.org/1998/Math/MathML" display="block"> X ( n ) = H ( n ) θ + V ( n ) https://www.w3.org/1999/xlink" content-type="black-white" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003353447/33d45e82-2e44-4e42-8180-04a739205e5f/content/math3_133_1_B.tif"/> where X(n), H(n) are data vectors and data matrices. V(n) is noise. H(n) ∈ ℝ n × p , X(n), V(n) ∈ ℝ n . If Rυ = Coυ(V(n)) and V(n) are iid zero mean Gaussian, then the MLE of θ based on data collected upto time n is given by https://www.w3.org/1998/Math/MathML" display="block"> θ ^ ( n ) = ( ∑ k = 1 n H ( k ) T R υ H ( k ) ) − 1 ( ∑ k = 1 n H ( n ) T R υ X ( k ) ) https://www.w3.org/1999/xlink" content-type="black-white" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003353447/33d45e82-2e44-4e42-8180-04a739205e5f/content/math3_133_2_B.tif"/>