What is Harmonic analysis?
'''Harmonic analysis''' is a branch of [[mathematics]] that looks at the theoretical foundations of [[digital signal processing]]. A continuous signal can be drawn as a [[wave]], or as a combination of several waves. [[Fourier transform]]s and [[Fourier series]] are among the main tools used for signal analysis. Today, this field has many uses, which also include [[quantum mechanics]] and [[neuroscience]]. In essence, harmonic analysis looks at [[locally compact group]]s. The [[Lebesgue measure]] is a way to assign a measurement to a [[subset]] of the [[Euclidean space]]. For [[real number]]s there is the [[Haar measure]], which can perform this task. This measure allows to use [[Fourier analysis]] to model the groups and their properties. The term ''harmonics'' is also related to [[Eigenvalue]]s, in the case where the [[frequency]] of one wave is an [[integer]] multiple of the frequency of another wave. This is the case of the [[Harmonics (music)|harmonics]] that are used for [[music|musical notes]]. Later the term was generalized. {{math-stub}} {{authority control}} [[Category:Digital signal processing]] [[Category:Harmonic analysis| ]]