The quantity 2W defines the resolution bandwidth for the spectral concentration problem and .

Among all sequences for a given T and W, is there a sequence for which the spectral concentration is maximum?

Fredholm equations arise naturally in the theory of signal processing, most notably as the famous spectral concentration problem popularized by David Slepian.

The largest eigenvalue of the above equation corresponds to the largest possible spectral concentration; the corresponding eigenvector is the required optimal sequence .

Prolate spheroidal wave functions whose domain is a (portion of) the surface of the unit sphere are more generally called "Slepian functions" (see also Spectral concentration problem).

The ratio of spectral concentration (irradiance or exitance) at a given wavelength to the concentration of a reference wavelength provides the relative SPD.

Not limited to time series, the spectral concentration problem can be reformulated to apply on the surface of the sphere by using spherical harmonics, for applications in geophysics and cosmology among others.

Brown BM, Eastham MSP, Spectral concentration for perturbed equations of harmonic oscillator type, LMS J. Comput.

Thomson chose the Slepian or discrete prolate spheroidal sequences as tapers since these vectors are mutually orthogonal and possess desirable spectral concentration properties (see the section on Slepian sequences).

Thus, the spectral concentration is strictly less than one, and there is no finite sequence for which the DTFT can be confined to a band [-W,W] and made to vanish outside this band.

The spectral concentration problem in Fourier analysis refers to finding a time sequence whose discrete Fourier transform is maximally localized on a given frequency interval, as measured by the spectral concentration.

Note that the prefix "spectral" is to be understood as an abbreviation of the phrase "spectral concentration of" which is understood and defined by the CIE as the "quotient of the radiometric quantity taken over an infinitesimal range on either side of a given wavelength, by the range".