Spectral slope

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Spectral slope

In astrophysics

Astrophysics

Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of astronomical objects such as galaxy, stars, planets, exoplanets, and the interstellar medium, as well as their interactions....
and planetary science

Planetary science

Planetary science, also known as planetology and closely related to planetary astronomy, is the science of planets, or planetary systems, and the solar system....
, spectral slope is a measure of dependence of the reflectance on the wavelength

Wavelength

In physics, wavelength is the distance between repeating units of a propagating wave of a given frequency. It is commonly designated by the Greek language letter lambda ....
. In digital signal processing

Digital signal processing

Digital signal processing is concerned with the representation of the signal s by a sequence of numbers or symbols and the processing of these signals....
, it is a measure of how quickly the spectrum of an audio sound tails off towards the high frequencies, calculated using a linear regression

Linear regression

Infrared

Infrared radiation is electromagnetic radiation whose wavelength is longer than that of visible light , but shorter than that of terahertz radiation and microwaves ....
spectrum

Electromagnetic spectrum

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In astrophysics

Astrophysics

Planetary science

Wavelength

Digital signal processing

Linear regression

Spectral slope in Astrophysics / Planetary Science

The visible and infrared

Infrared

Infrared radiation is electromagnetic radiation whose wavelength is longer than that of visible light , but shorter than that of terahertz radiation and microwaves ....
spectrum

Electromagnetic spectrum

The electromagnetic spectrum is the range of all possible electromagnetic radiation frequencies. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation from that particular object....
of the reflected sunlight is used to infer physical and chemical properties of the surface of a body. Some objects are brighter (reflect more) in longer wavelengths (red). Consequently, in visible light they will appear redder than objects showing no dependence of reflectance on the wavelength.

The diagram illustrates three slopes:

a red slope, the reflectance is increasing with the wavelengths
flat spectrum (in black)
And a blue slope, the reflectance actually diminishing with the wavelengths

The slope is typically expressed in percentage increase of reflectance (i.e. reflexivity) per unit of wavelength: %/100 nm (or % /1000 Å)

The slope is mostly used in near infrared part of the spectrum while colour indices

Color index

In astronomy, the color index is a simple numerical expression that determines the color of an object, which in the case of a star gives its temperature....
are commonly used in the visible part of the spectrum.

The trans-Neptunian object

Trans-Neptunian object

A trans-Neptunian object is any object in the solar system that orbits the sun at a greater distance on average than Neptune . The Kuiper belt, scattered disk, and Oort cloud are three divisions of this volume of space....
Sedna

90377 Sedna

90377 Sedna is a trans-Neptunian object and a likely dwarf planet, discovered by Michael E. Brown , Chad Trujillo and David L. Rabinowitz on November 14, 2003....
is a typical example of a body showing a steep red slope (20%/100nm) while Orcus'

90482 Orcus

90482 Orcus is a Kuiper Belt object and a likely dwarf planet that was discovered by Michael E. Brown of California Institute of Technology, Chad Trujillo of the Gemini Observatory, and David L....
spectrum appears flat in near infra-red.

Spectral slope in audio

The spectral "slope" of many natural audio signals (their tendency for to have less energy at high frequencies) has been known for many years , and the fact that this slope is related to the nature of the sound source. One way to quantify this is by applying linear regression

Linear regression

In statistics, linear regression is used for two things;Linear regression is a form of regression analysis in which the relationship between one or more independent variables and another variable, called the dependent variable, is modeled by a least squares function, called linear regression equation....
to the Fourier magnitude spectrum of the signal, which produces a single number indicating the slope of the line-of-best-fit through the spectral data .

Alternative ways to characterise a sound signal's distribution of energy vs frequency include spectral rolloff, spectral centroid

Spectral centroid

The spectral centroid is a measure used in digital signal processing to characterise an audio spectrum. It indicates where the "center of mass" of the spectrum is....
.