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 transforms and
Fourier series are among the main tools used for signal analysis. Today, this field has many uses, which also include
quantum mechanics and
In essence, harmonic analysis looks at
locally compact groups. The
Lebesgue measure is a way to assign a measurement to a
subset of the
Euclidean space. For
real numbers 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
Eigenvalues, 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 that are used for
musical notes. Later the term was generalized.