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Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency.The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals.
The total harmonic distortion (THD or THDi) is a measurement of the harmonic distortion present in a signal and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency. Distortion factor, a closely related term, is sometimes used as a synonym.
A weakly harmonic function coincides almost everywhere with a strongly harmonic function, and is in particular smooth. A weakly harmonic distribution is precisely the distribution associated to a strongly harmonic function, and so also is smooth. This is Weyl's lemma. There are other weak formulations of Laplace's equation that are often useful.
The harmonic number with = ⌊ ⌋ (red line) with its asymptotic limit + (blue line) where is the Euler–Mascheroni constant.. In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: [1] = + + + + = =.
When that interval is [,], the applicable reconstruction formula is the Whittaker–Shannon interpolation formula. This is a cornerstone in the foundation of digital signal processing . Another reason to be interested in S 1 T ( f ) {\displaystyle S_{\tfrac {1}{T}}(f)} is that it often provides insight into the amount of aliasing caused by the ...
A harmonic is any member of the harmonic series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The reason a fundamental is also considered a harmonic is because it is 1 times itself. [11] The fundamental is the frequency at which the entire wave vibrates.
A series of mathematicians applying harmonic analysis to number theory, most notably Martin Eichler, Atle Selberg, Robert Langlands, and James Arthur, have generalised the Poisson summation formula to the Fourier transform on non-commutative locally compact reductive algebraic groups with a discrete subgroup such that / has finite volume.
Harmonic analysis – Study of superpositions in mathematics; Harmonics (electrical power) – Sinusoidal wave whose frequency is an integer multiple; Harmonic generation – Nonlinear optical process; Harmonic oscillator – Physical system that responds to a restoring force inversely proportional to displacement; Harmony – Aspect of music
