astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the he ...

and

planetary science Planetary science (or more rarely, planetology) is the scientific study of planets (including Earth), celestial bodies (such as moons, asteroids, comets) and planetary systems (in particular those of the Solar System) and the processes of the ...

, spectral slope, also called spectral gradient, is a measure of dependence of the

reflectance The reflectance of the surface of a material is its effectiveness in Reflection (physics), reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the respon ...

on the

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...

. In

digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner ar ...

, it is a measure of how quickly the spectrum of an audio sound tails off towards the high frequencies, calculated using a

linear regression In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is ...

.G. Peeters
A large set of audio features for sound description
tech. rep., IRCAM, 2004. TheSpectralSlope

Spectral slope in astrophysics and planetary science

The visible and

infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from aroun ...

spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of color ...

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 (spectral gradient) is defined as: :

S = \frac

:where

R_, R_

is the reflectance measured with filters F₀, F₁ having the central wavelengths λ₀ and λ₁, respectively. 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 are commonly used in the visible part of the spectrum. The

trans-Neptunian object A trans-Neptunian object (TNO), also written transneptunian object, is any minor planet in the Solar System that orbits the Sun at a greater average distance than Neptune, which has a semi-major axis of 30.1 astronomical units (au). Typicall ...

Sedna is a typical example of a body showing a steep red slope (20%/100 nm) while Orcus' spectrum appears flat in near infra-red.

Spectral slope in audio

The spectral "slope" of many natural audio signals (their tendency 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

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 The spectral centroid is a measure used in digital signal processing to characterise a spectrum. It indicates where the center of mass of the spectrum is located. Perceptually, it has a robust connection with the impression of brightness of a soun ...

Animals that can sense spectral slope

The dung beetle can see the spectral gradient of the sky and polarised light, and they used this to navigate. Desert ants Cataglyphis use the polarization and spectral skylight gradients to navigate.

References

{{Reflist Planetary science Digital signal processing

Spectral slope in astrophysics and planetary science

Spectral slope in audio

Animals that can sense spectral slope

See also

References