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What (who) is graded filter - definition
![The 80A filter, mainly used to correct for the excessive redness of [[tungsten]] lighting, can also be used to oversaturate scenes that already have blue. The photo on the left was shot with a polarizer, while the one on the right was shot with a polarizer and an 80A filter.](https://commons.wikimedia.org/wiki/Special:FilePath/80a comparison.jpg?width=200 "The 80A filter, mainly used to correct for the excessive redness of [[tungsten]] lighting, can also be used to oversaturate scenes that already have blue. The photo on the left was shot with a polarizer, while the one on the right was shot with a polarizer and an 80A filter.")
![The ''LOMO effect'' imitates photos made with a low-cost Russian camera brand, named "LOMO". It is approximated by saturated central colors, blurred periphery, and darkened corners and edges ([[vignetting]]).}} effect.](https://commons.wikimedia.org/wiki/Special:FilePath/Verblühende Sauerkirsche.jpg?width=200 "The ''LOMO effect'' imitates photos made with a low-cost Russian camera brand, named \"LOMO\". It is approximated by saturated central colors, blurred periphery, and darkened corners and edges ([[vignetting]]).}} effect.")
.svg?width=200 "The frequency response of a fourth-order elliptic low-pass filter with '''ε''' = 0.5 and '''ξ''' = 1.05. Also shown are the minimum gain in the passband and the maximum gain in the stopband, and the transition region between normalized frequency 1 and '''ξ'''")
.svg?width=200 "A closeup of the transition region of the above plot.")
![Log of the absolute value of the gain of an 8th order elliptic filter in [[complex frequency space]] (s = σ + jω) with ε = 0.5, ξ = 1.05 and ω<sub>0</sub> = 1. The white spots are poles and the black spots are zeroes. There are a total of 16 poles and 8 double zeroes. What appears to be a single pole and zero near the transition region is actually four poles and two double zeroes as shown in the expanded view below. In this image, black corresponds to a gain of 0.0001 or less and white corresponds to a gain of 10 or more.](https://commons.wikimedia.org/wiki/Special:FilePath/Elliptic Filter s-Plane Response (8th Order).svg?width=200 "Log of the absolute value of the gain of an 8th order elliptic filter in [[complex frequency space]] (s = σ + jω) with ε = 0.5, ξ = 1.05 and ω<sub>0</sub> = 1. The white spots are poles and the black spots are zeroes. There are a total of 16 poles and 8 double zeroes. What appears to be a single pole and zero near the transition region is actually four poles and two double zeroes as shown in the expanded view below. In this image, black corresponds to a gain of 0.0001 or less and white corresponds to a gain of 10 or more.")
.svg?width=200 "An expanded view in the transition region of the above image, resolving the four poles and two double zeroes.")
Wikipedia
In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups such that . The index set is usually the set of nonnegative integers or the set of integers, but can be any monoid. The direct sum decomposition is usually referred to as gradation or grading.
A graded module is defined similarly (see below for the precise definition). It generalizes graded vector spaces. A graded module that is also a graded ring is called a graded algebra. A graded ring could also be viewed as a graded -algebra.
The associativity is not important (in fact not used at all) in the definition of a graded ring; hence, the notion applies to non-associative algebras as well; e.g., one can consider a graded Lie algebra.
