A function is said to be piecewise constant if it is locally constant in connected regions separated by a possibly infinite number of lower-dimensional boundaries. The Heaviside step function, rectangle function, and square wave are examples of one-dimensional piecewise constant functions. Examples in two dimensions include and (illustrated above) for a complex number, the real part, and the floor function. The nearest integer function is also piecewise constant.
Piecewise Constant Function
See also
Constant Function, Decreasing Function, Increasing Function, Piecewise Function, Piecewise Linear FunctionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Piecewise Constant Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PiecewiseConstantFunction.html