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:

    “We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the child’s life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.”
    —Selma H. Fraiberg (20th century)

    “A novel which survives, which withstands and outlives time, does do something more than merely survive. It does not stand still. It accumulates round itself the understanding of all these persons who bring to it something of their own. It acquires associations, it becomes a form of experience in itself, so that two people who meet can often make friends, find an approach to each other, because of this one great common experience they have had ...”
    —Elizabeth Bowen (1899–1973)