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- Harmonic_analysis abstract "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 signal processing, quantum mechanics, and neuroscience.The term "harmonics" originated as the ancient Greek word, "harmonikos," meaning "skilled in music." It arose in physical eigenvalue-problems 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. This is a very elementary form of an uncertainty principle in a harmonic analysis setting. See also: Convergence of Fourier series.Fourier series can be conveniently studied in the context of Hilbert spaces, which provides a connection between harmonic analysis and functional analysis.".
- Harmonic_analysis thumbnail Light_wave_harmonic_diagram.jpg?width=300.
- Harmonic_analysis wikiPageID "14147".
- Harmonic_analysis wikiPageRevisionID "599810220".
- Harmonic_analysis hasPhotoCollection Harmonic_analysis.
- Harmonic_analysis subject Category:Harmonic_analysis.
- Harmonic_analysis comment "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).".
- Harmonic_analysis label "Analisi armonica".
- Harmonic_analysis label "Analiza harmoniczna".
- Harmonic_analysis label "Analyse harmonique (mathématiques)".
- Harmonic_analysis label "Análise harmónica".
- Harmonic_analysis label "Análisis armónico".
- Harmonic_analysis label "Fourieranalyse".
- Harmonic_analysis label "Harmonic analysis".
- Harmonic_analysis label "Harmonische Analyse".
- Harmonic_analysis label "Гармонический анализ".
- Harmonic_analysis label "تحليل توافقي".
- Harmonic_analysis label "傅里叶分析".
- Harmonic_analysis label "調和解析".
- Harmonic_analysis sameAs Harmonische_Analyse.
- Harmonic_analysis sameAs Análisis_armónico.
- Harmonic_analysis sameAs Analyse_harmonique_(mathématiques).
- Harmonic_analysis sameAs Analisis_Fourier.
- Harmonic_analysis sameAs Analisi_armonica.
- Harmonic_analysis sameAs 調和解析.
- Harmonic_analysis sameAs 조화해석학.
- Harmonic_analysis sameAs Fourieranalyse.
- Harmonic_analysis sameAs Analiza_harmoniczna.
- Harmonic_analysis sameAs Análise_harmónica.
- Harmonic_analysis sameAs m.03ny_.
- Harmonic_analysis sameAs Q876215.
- Harmonic_analysis sameAs Q876215.
- Harmonic_analysis wasDerivedFrom Harmonic_analysis?oldid=599810220.
- Harmonic_analysis depiction Light_wave_harmonic_diagram.jpg.
- Harmonic_analysis isPrimaryTopicOf Harmonic_analysis.
