Harmonic functions | Integral transforms | Signal processing | Singular integrals
In mathematics and in signal processing, the Hilbert transform is a specific linear operator that takes a function, u(t) of a real variable and produces another function of a real variable H(u)(t). This linear operator is given by convolution with the function (see ). The Hilbert transform has a particularly simple representation in the frequency domain: It imparts a phase shift of ±90° (π⁄2 radians) to every frequency component of a function, the sign of the shift depending on the sign of the frequency (see ). The Hilbert transform is important in signal processing, where it is a component of the analytic representation of a real-valued signal u(t). The Hilbert transform was first introduced by David Hilbert in this setting, to solve a special case of the Riemann–Hilbert problem for analytic functions. (Wikipedia).
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/2toQ.
From playlist 3D printing
Functional Analysis Lecture 08 2014 02 13 The Hilbert Transform
Poisson kernel; conjugate Poisson kernel; Poisson integral representation; conjugate Poisson integral representation. Connection with Cauchy integral. Definition of Hilbert transform; orthogonal projection; Hilbert transform of an L^2 function realized as a principal value integral.
From playlist Course 9: Basic Functional and Harmonic Analysis
Introduction to the z-Transform
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduces the definition of the z-transform, the complex plane, and the relationship between the z-transform and the discrete-time Fourier transfor
From playlist The z-Transform
In this video you will learn about the Hilbert transform, which can be used to compute the "analytic signal" (a complex time series from which instantaneous power and phase angles can be extracted). The video uses files you can download from https://github.com/mikexcohen/ANTS_youtube_vide
From playlist OLD ANTS #4) Time-frequency analysis via other methods
The Fourier Transform and Derivatives
This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow
From playlist Fourier
Electrical Engineering: Ch 19: Fourier Transform (2 of 45) What is a Fourier Transform? Math Def
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the mathematical definition and equation of a Fourier transform. Next video in this series can be seen at: https://youtu.be/yl6RtWp7y4k
From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM
Dimitri Grigoryev - A Tropical Version of Hilbert Polynomial
We define Hilbert function of a semiring ideal of tropical polynomials in n variables. For n=1 we prove that it is the sum of a linear function and a periodic function (for sufficiently large values). The leading coefficient of the linear function equals the tropical entropy of the ideal.
From playlist Combinatorics and Arithmetic for Physics: special days
Functional Analysis Lecture 12 2014 03 04 Boundedness of Hilbert Transform on Hardy Space (part 1)
Dyadic Whitney decomposition needed to extend characterization of Hardy space functions to higher dimensions. p-atoms: definition, have bounded Hardy space norm; p-atoms can also be used in place of atoms to define Hardy space. The Hilbert Transform is bounded from Hardy space to L^1: b
From playlist Course 9: Basic Functional and Harmonic Analysis
To Understand the Fourier Transform, Start From Quantum Mechanics
Develop a deep understanding of the Fourier transform by appreciating the critical role it plays in quantum mechanics! Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up Sign up for my newsletter for additional physics lessons: https://www.physicswithelliot.c
From playlist Physics Mini Lessons
This video lesson is part of a complete course on neuroscience time series analyses. The full course includes - over 47 hours of video instruction - lots and lots of MATLAB exercises and problem sets - access to a dedicated Q&A forum. You can find out more here: https://www.udemy.
From playlist NEW ANTS #3) Time-frequency analysis
On the dyadic Hilbert transform – Stefanie Petermichl – ICM2018
Analysis and Operator Algebras Invited Lecture 8.10 On the dyadic Hilbert transform Stefanie Petermichl Abstract: The Hilbert transform is an average of dyadic shift operators. These can be seen as a coefficient shift and multiplier in a Haar wavelet expansion or as a time shifted operat
From playlist Analysis & Operator Algebras
Comparing wavelet, filter-Hilbert, and STFFT
This video lesson is part of a complete course on neuroscience time series analyses. The full course includes - over 47 hours of video instruction - lots and lots of MATLAB exercises and problem sets - access to a dedicated Q&A forum. You can find out more here: https://www.udemy.
From playlist NEW ANTS #3) Time-frequency analysis
The computational theory of Riemann–Hilbert problems (Lecture 4) by Thomas Trogdon
Program : Integrable Systems in Mathematics, Condensed Matter and Statistical Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan Lecture Hall, ICT
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Twisted real structures for spectral triples
Talk by Adam Magee in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 31, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Alexander Goncharov - 3/4 Quantum Geometry of Moduli Spaces of Local Systems...
Quantum Geometry of Moduli Spaces of Local Systems and Representation Theory Lectures 1-3 are mostly based on our recent work with Linhui Shen. Given a surface S with punctures and special points on the boundary considered modulo isotopy, and a split semi-simple adjoint group G, we defin
From playlist Alexander Goncharov - Quantum Geometry of Moduli Spaces of Local Systems and Representation Theory
Robert Wald - The Memory Effect and Infrared Divergences - IPAM at UCLA
Recorded 27 October 2021. Robert Wald of the University of Chicago presents "The Memory Effect and Infrared Divergences" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: The "memory effect" is the permanent relative displacement of test particles after th
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
Empirical Mode Decomposition (1D, univariate approach)
Introduction to the Empirical Mode Decomposition - EMD - (one-dimensional, univariate version), which is a data decomposition method for non-linear and non-stationary data. This video covers the main features of the EMD and the working principle of the algorithm. The EMD is briefly compar
From playlist Summer of Math Exposition Youtube Videos
Stephanos Venakides: Rigorous semiclassical asymptotics for integrable systems
The title of the lecture is shortened to comply with Youtubes' title policy. The original title of this lecture is "Rigorous semiclassical asymptotics for integrable systems:The KdV and focusing NLS cases". Programme for the Abel Lectures 2005: 1. "Abstract Phragmen-Lindelöf theorem & Sa
From playlist Abel Lectures