Definitions for harmonic analysis
har·mon·ic ana·ly·sis

Princeton's WordNetRate this definition:0.0 / 0 votes

1. Fourier analysis, harmonic analysisnoun

   analysis of a periodic function into a sum of simple sinusoidal components

WiktionaryRate this definition:0.0 / 0 votes

1. harmonic analysisnoun

   A study of the representation of functions or signals as the superposition of basic waves, involving the notions of harmonic functions, trigonometric series, Fourier series, Fourier transforms, almost periodic functions, and others.

WikipediaRate this definition:0.0 / 0 votes

1. Harmonic analysis

   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).

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1. harmonic analysis

   Harmonic analysis is a branch of mathematics that studies the transformation of signals or functions using sinusoids or other basic waveforms. It involves the representation of functions or signals as the superposition of basic waves and the study of their properties. It is used in many areas of mathematics, including number theory, signal processing, quantum mechanics, and neuroscience.

WikidataRate this definition:0.0 / 0 votes

1. Harmonic analysis

   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. In the past two centuries, it has become a vast subject with applications in areas as diverse as signal processing, quantum mechanics, and neuroscience. The term "harmonics" originated in physical eigenvalue problems, to mean waves whose frequencies are integer multiples of one another, as are the frequencies of the harmonics on stringed musical instruments, but the term has been generalized beyond its original meaning. The classical Fourier transform on R 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, then its Fourier transform is never compactly supported. This is a very elementary form of an uncertainty principle in a harmonic analysis setting.

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How to say harmonic analysis in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of harmonic analysis in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of harmonic analysis in Pythagorean Numerology is: 1

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=harmonic analysis
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Harmonic_Analysis
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Harmonic_Analysis
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=harmonic analysis