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)

    This conflict between the powers of love and chastity ... it ended apparently in the triumph of chastity. Love was suppressed, held in darkness and chains, by fear, conventionality, aversion, or a tremulous yearning to be pure.... But this triumph of chastity was only an apparent, a pyrrhic victory. It would break through the ban of chastity, it would emerge—if in a form so altered as to be unrecognizable.
    Thomas Mann (1875–1955)