Dirac comb

In mathematics, a Dirac comb (also known as an impulse train and sampling function in electrical engineering) is a periodic tempered distribution constructed from Dirac delta functions

for some given period T. The symbol , where the period is omitted, represents a Dirac comb of unit period. Some authors, notably Bracewell 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 letter sha Ш). Because the Dirac comb function is periodic, it can be represented as a Fourier series: