Heaviside Step Function - Discrete Form

Discrete Form

An alternative form of the unit step, as a function of a discrete variable n:

where n is an integer. Unlike the usual (not discrete) case, the definition of H is significant.

The discrete-time unit impulse is the first difference of the discrete-time step

This function is the cumulative summation of the Kronecker delta:

where

is the discrete unit impulse function.

Read more about this topic:  Heaviside Step Function

Famous quotes containing the words discrete and/or form:

    The mastery of one’s phonemes may be compared to the violinist’s mastery of fingering. The violin string lends itself to a continuous gradation of tones, but the musician learns the discrete intervals at which to stop the string in order to play the conventional notes. We sound our phonemes like poor violinists, approximating each time to a fancied norm, and we receive our neighbor’s renderings indulgently, mentally rectifying the more glaring inaccuracies.
    W.V. Quine (b. 1908)

    In America every woman has her set of girl-friends; some are cousins, the rest are gained at school. These form a permanent committee who sit on each other’s affairs, who “come out” together, marry and divorce together, and who end as those groups of bustling, heartless well-informed club-women who govern society. Against them the Couple of Ehepaar is helpless and Man in their eyes but a biological interlude.
    Cyril Connolly (1903–1974)