Undergrad Eigenspectra and Empirical Orthogonal Functions

[ecastro]

Are the Eigenspectra (a spectrum of eigenvalues) and the Empirical Orthogonal Functions (EOFs) the same?

I have known that both can be calculated through the Singular Value Decomposition (SVD) method.

Thank you in advance.

 

[akeleti8]

Hi there. Eigenspectra is a spuctrum of eigenvalues. eigenvalues are values of a scalar

so that [PLAIN]https://upload.wikimedia.org/math/3/6/4/364442fc3d24dc6d566c98cfa307b1f0.pngx=Bx. B is any given function. The eigenvalues of a matrix J can be found by finding det( J - [PLAIN]https://upload.wikimedia.org/math/3/6/4/364442fc3d24dc6d566c98cfa307b1f0.pngI). empirical orthogonal functions are a means of decomposing a dataset in terms of orthogonal basis functions. This is not what eigenspectra are.

This is a congenial problem for development for an anorthosite loving kid. i use wolfram alpha to help me with this problem. .

 

[ecastro]

From an article I have been reading, the eigenspectra they discuss can be calculated from a collection of data. They then use these eigenspectra to reconstruct some parts of the data.

$E = a_1 \hat{e}_1 + a_2 \hat{e}_2 + a_3 \hat{e}_3 + \cdots$,

where $E$ is the reconstructed signal, $a_1, a_2, a_3, ...$ are coefficients, and $\hat{e}_1, \hat{e}_2, \hat{e}_3, ...$ are what they call the eigenspectra. Isn't this also how the Empirical Orthogonal Functions are used to reconstruct a signal or data?

 

[Stephen Tashi]

From an article I have been reading,

Is the article available online ? What's the article about ?

 

[ecastro]

The article's title is "Accuracy of Spectrum Estimate in Flourescence Spectral Microscopy with Spectral Filters". The article is about the reconstruction of a sample's spectrum.