- Hilbert spectral analysis
**Hilbert spectral analysis**is a signal analysis method applying theHilbert transform to compute theinstantaneous frequency of signals according to

:$omega=frac\{d\; heta(t)\}\{dt\}.,$After performing theHilbert transform on each signal, we can express the data in the following form::$X(t)=sum\_\{j=1\}^\{n\}a\_j(t)exp(iintomega\_j(t)dt).,$This equation gives both the amplitude and the frequency of each component as functions of time. It also enables us to represent the amplitude and the

instantaneous frequency as functions of time in a three-dimensional plot, in which the amplitude can be contoured on the frequency-time plane. This frequency-time distribution of the amplitude is designated as the Hilbert amplitude spectrum, or simplyHilbert spectrum .Hilbert spectral analysis method is an important part of

Hilbert-Huang transform .**See also***

Hilbert transform

*Hilbert-Huang transform

*Hilbert spectrum **References***Alan V. Oppenheim and Ronald W. Schafer, "Discrete-Time Signal Processing"," Prentice-Hall Signal Processing Series, 2 ed., 1999.

*Huang, et al. "The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis." "Proc. R. Soc. Lond. A" (1998)

**454**, 903–995 ( [*http://keck.ucsf.edu/~schenk/Huang_etal98.pdf Link*] )

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