Computing Discrete Convolution in terms of unit step function

1. What is discrete unit step function?
2. Which function is the integral of the unit step function?

What is discrete unit step function?

The unit step, both for continuous and discrete time, is zero for negative time and unity for positive time. In discrete time the unit step is a well-defined sequence, whereas in continuous time there is the mathematical complication of a discontinuity at the origin.

Which function is the integral of the unit step function?

In other words, the integral of a unit step is a "ramp" function. This function is 0 for all values that are less than zero, and becomes a straight line at zero with a slope of +1.