What Is Zero Crossing?

In mathematics and engineering, "zero crossing" is the point at which the sign of a function changes, either from negative to positive or from positive to negative.

Illustration

• One illustration involves a ball thrown from ground level at a given (initial) speed.

  For example, use 96 feet per second as the initial speed. In that case, after one second, 1(t), the ball would be 80 feet above the ground. To find the position of the ball at any given number of seconds after it is thrown, you must account for gravity, as well as this initial velocity.

  It would reach its apogee at 3(t), and would hit the ground again (returning to zero) at 6(t).

  If there were a hole dug into the ground at the point of landing, so that the ball continued downward into negative altitude, then we could also describe 6(t) as the zero crossing.

Definition

• The term zero crossing derives from the graphing of functions, when the function, depicted as a curve, crosses a line that represents the x-axis, or zero on the y-axis.

Significance

• A sine curve, in particular, is a commonly graphed S-shaped wave that passes its zero crossing an indefinite number of times.