In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a Dirac comb (also known as an impulse train and sampling function in electrical engineering

Electrical engineering

Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

) is a periodic

Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...

 Schwartz distribution constructed from Dirac delta function

Dirac delta function

The Dirac delta function, or δ function, is a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one. It was introduced by theoretical...

s


for some given period T. Some authors, notably Bracewell

Ronald N. Bracewell

Ronald Newbold Bracewell AO was the Lewis M. Terman Professor of Electrical Engineering, Emeritus of the at Stanford University.- Education :...

 as well as some textbook authors in electrical engineering and circuit theory, refer to it as the Shah function (possibly because its graph resembles the shape of the Cyrillic

Cyrillic alphabet

The Cyrillic script or azbuka is an alphabetic writing system developed in the First Bulgarian Empire during the 10th century AD at the Preslav Literary School...

 letter sha

Sha

For other uses, see Sha .Sha is a letter of the Cyrillic alphabet. It commonly represents the voiceless postalveolar fricative , like the pronunciation of ⟨sh⟩ in "sheep", or the somewhat similar voiceless retroflex fricative . It is used in every variation of the Cyrillic alphabet, for Slavic and...

 Ш).