Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two centuries, it has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience. The term "harmonics" originated as the Ancient Greek word harmonikos, meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are integer multiples of one another, as are the frequencies of the harmonics of music notes, but the term has been generalized beyond its original meaning. The classical Fourier transform on Rn is still an area of ongoing research, particularly concerning Fourier transformation on more general objects such as tempered distributions. For instance, if we impose some requirements on a distribution f, we can attempt to translate these requirements in terms of the Fourier transform of f. The Paley–Wiener theorem is an example of this. The Paley–Wiener theorem immediately implies that if f is a nonzero distribution of compact support (these include functions of compact support), then its Fourier transform is never compactly supported (i.e. if a signal is limited in one domain, it is unlimited in the other). This is a very elementary form of an uncertainty principle in a harmonic-analysis setting. Fourier series can be conveniently studied in the context of Hilbert spaces, which provides a connection between harmonic analysis and functional analysis. There are four versions of the Fourier transform, dependent on the spaces that are mapped by the transformation (discrete/periodic–discrete/periodic: discrete Fourier transform, continuous/periodic–discrete/aperiodic: Fourier series, discrete/aperiodic–continuous/periodic: discrete-time Fourier transform, continuous/aperiodic–continuous/aperiodic: Fourier transform). (Wikipedia).
An example of a harmonic series.
From playlist Advanced Calculus / Multivariable Calculus
Terence Tao: The circle method from the perspective of higher order Fourier analysis
Higher order Fourier analysis is a collection of results and methods that can be used to control multilinear averages (such as counts for the number of four-term progressions in a set) that are out of reach of conventional linear Fourier analysis methods (i.e., out of reach of the circle m
From playlist Harmonic Analysis and Analytic Number Theory
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From playlist Lecture Recordings
If the Laplacian of a function is zero everywhere, it is called Harmonic. Harmonic functions arise all the time in physics, capturing a certain notion of "stability", whenever one point in space is influenced by its neighbors.
From playlist Fourier
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Solving an example problem of simple harmonic oscillation, which requires calculating the solution to a second order ordinary differential equation.
From playlist Physics ONE
Complex Analysis 04: Harmonic Functions
Complex Analysis 04. Harmonic functions and the harmonic conjugate
From playlist MATH2069 Complex Analysis
Complex analysis: Harmonic functions
This lecture is part of an online undergraduate course on complex analysis. We study the question: when is a function u the real part of a holomorphic function w=u+iv? An easy necessary condition is that u mist be harmonic. We use the Caucy-Riemann equations to show that this condition is
From playlist Complex analysis
Harmonic analytic geometry in high dimensions – Empirical models – Ronald Coifman – ICM2018
Plenary Lecture 10 Harmonic analytic geometry on subsets in high dimensions – Empirical models Ronald Coifman Abstract: We describe a recent evolution of Harmonic Analysis to generate analytic tools for the joint organization of the geometry of subsets of ℝⁿ and the analysis of functions
From playlist Plenary Lectures
Lecture 21 (CEM) -- RCWA Tips and Tricks
Having been through the formulation and implementation of RCWA in previous lectures, this lecture discussed several miscellaneous topics including modeling 1D gratings with 3D RCWA, formulation of a 2D RCWA that incorporates fast Fourier factorization, RCWA for curved structures, truncatin
From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering
Power Quality and Harmonic Analysis | What Is 3-Phase Power? -- Part 7
In AC electrical systems, a deviation in an AC waveform from a perfect sinusoid with nominal magnitude and frequency lowers the quality of supply, which can adversely affect system operation. Understanding what types of power quality issues occur and how to measure those issues is importan
From playlist What Is 3-Phase Power?
MIT Electronic Feedback Systems (1985) View the complete course: http://ocw.mit.edu/RES6-010S13 Instructor: James K. Roberge License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Electronic Feedback Systems (1985)
The Physics of Rock I: The Motion of a Guitar String
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From playlist The Physics of Rock
CDIS 4017 - Clinical Instrumentation Part 1 (done)
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From playlist ETSU: CDIS 4017 - Speech and Hearing Science I | CosmoLearning Audiology
NIPS 2011 Music and Machine Learning Workshop: Learning melodic analysis rules
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From playlist NIPS 2011 Music and Machine Learning Workshop
Data Science - Part XVI - Fourier Analysis
For downloadable versions of these lectures, please go to the following link: http://www.slideshare.net/DerekKane/presentations https://github.com/DerekKane/YouTube-Tutorials This lecture provides an overview of the Fourier Analysis and the Fourier Transform as applied in Machine Learnin
From playlist Data Science
Brief introduction to the Langlands program
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From playlist Popular presentations
How to find a Harmonic Conjugate Complex Analysis
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to find a Harmonic Conjugate Complex Analysis
From playlist Complex Analysis