Hilbert spectrum [SEP] named after
Hilbert spectrum
The Hilbert spectrum (sometimes referred to as the Hilbert amplitude spectrum), named after David Hilbert, is a statistical tool that can help in distinguishing among a mixture of moving signals. The spectrum itself is decomposed into its component sources using independent component analysis. The separation of the combined effects of unidentified sources (blind signal separation) has applications in climatology, seismology, and biomedical imaging.
Conceptual summary.
The Hilbert spectrum is computed by way of a 2-step process consisting of:
- Preprocessing a
of and
formula_5
The instantaneous angle frequency is then defined as
formula_6
From this, we can define the Hilbert Spectrum for formula_7 as
formula_8
The Hilbert Spectrum of formula_1 is then given by
formula_10
Definition of Marginal Hilbert Spectrum.
A two dimensional representation of a Hilbert Spectrum, called Marginal Hilbert Spectrum, is defined as
formula_11
where formula_12 is the length of the sampled signal formula_1. The Marginal Hilbert Spectrum show the total energy that each frequency value contribute with.
Applications of the