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, James Keeler, said, astrophysics "seeks to ascertain the ...

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 ...

, 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 reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic ...

on the

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

. 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 are a ...

, 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 statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...

.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 that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...

spectrum A spectrum (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...

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 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. The lower the color index, the more blue (or hotter) the object is. Conversely, the larg ...

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 an orbital semi-major axis of 30.1 astronomical units (AU). ...

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 In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter o ...

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