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Spectral concentration problem information


The three leading Slepian sequences for T=1000 and 2WT=6. Note that each higher order sequence has an extra zero crossing.

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

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Spectral concentration problem

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The spectral concentration problem in Fourier analysis refers to finding a time sequence of a given length whose discrete Fourier transform is maximally...

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Fredholm integral equation

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the theory of signal processing, for example as the famous spectral concentration problem popularized by David Slepian. The operators involved are the...

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Multitaper

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. The quantity 2W defines the resolution bandwidth for the spectral concentration problem and W ∈ ( 0 , f N ) {\displaystyle W\in (0,f_{N})} . When l = m...

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Prolate spheroidal wave function

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) {\displaystyle S_{0n}(c,t/T)} introduced above. (See also Spectral concentration problem.) Pioneering work in this area was performed by Slepian and...

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Emanuel Milman

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Solves Triple Bubble Problem and More in Quanta magazine. The Role of Convexity in Isoperimetry, Spectral-Gap and Concentration - A Talk by Emanuel Milman...

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Finite element method

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element method. Spectral element methods combine the geometric flexibility of finite elements and the acute accuracy of spectral methods. Spectral methods are...

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Atomic absorption spectroscopy

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In analytical chemistry the technique is used for determining the concentration of a particular element (the analyte) in a sample to be analyzed. AAS...

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Normalized difference vegetation index

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the precursor to the Landsat program. These early sensors had minimal spectral resolution, but tended to include bands in the red and near-infrared, which...

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Inverse problem

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the controls on plant-matter decay. The linear inverse problem is also the fundamental of spectral estimation and direction-of-arrival (DOA) estimation...

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Color

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Animal perception of color originates from different light wavelength or spectral sensitivity in cone cell types, which is then processed by the brain. Colors...

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Spectroscopy

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radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave...

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Brownian motion

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the Kronecker delta. The spectral content of a stochastic process X t {\displaystyle X_{t}} can be found from the power spectral density, formally defined...

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Imaging spectroscopy

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relative concentrations, subsequently the assignment of the proportional contribution of mixed pixel signals (e.g., the spectral unmixing problem), the derivation...

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Emissivity

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body at the same temperature as that surface. Spectral hemispherical emissivity in frequency and spectral hemispherical emissivity in wavelength of a surface...

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Random matrix

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cavity method, or the replica method to compute quantities like traces, spectral densities, or scalar products between eigenvectors. Many physical phenomena...

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Ellipsometry

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composition, roughness, thickness (depth), crystalline nature, doping concentration, electrical conductivity and other material properties. It is very sensitive...

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Detection limit

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limit is the adequacy and the accuracy of the model used to predict concentration from the raw analytical signal. As a typical example, from a calibration...

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Radon

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sources of indoor radon, determinants of concentration, health effects, and mitigation approaches. In the US, the problem of indoor radon received widespread...

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False color

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(metameric failure): Different spectral sensitivities of the human eye and of an image capture device (e.g. a camera). Different spectral emissions / reflections...

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Remote sensing in geology

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limited due to signal engineering problem. One can never obtain data with maximum resolutions in all spatial, spectral and radiometric resolutions due to...

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Excimer lamp

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range of wavelengths in the ultraviolet (UV) and vacuum ultraviolet (VUV) spectral regions. Operation of an excimer lamp is based on the formation of excited...

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Immunofluorescence

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or DyLight Fluors. Other problems that may arise when using immunofluorescence techniques include autofluorescence, spectral overlap and non-specific...

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Glechoma hederacea

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Elzenga, J. T. M. (2015). "Competition for pollinators and intra-communal spectral dissimilarity of flowers". Plant Biology. 18 (1): 56–62. doi:10.1111/plb...

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Gas detector

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gas. Passive IR imaging sensors measure spectral changes at each pixel in an image and look for specific spectral signatures that indicate the presence...

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Phosphorus deficiency

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diagnostic problems as a result of interference from other present compounds and elements. Additional phosphorus detection methods such as spectral radiance...

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