Why is the signum function $=2u(t) - 1$?

1. Is signum function even or odd?
2. What is the equation for signum function?
3. Why is signum function discontinuous?
4. How signum function is expressed in terms of unit step function?

Is signum function even or odd?

In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.

What is the equation for signum function?

Properties of signum function

The function sgn x yielding a real number, is defined by: sgn x = 1 if 0 < x, sgn x = -1 if x < 0, sgn x = 0, otherwise.

Why is signum function discontinuous?

It has a jumped discontinuity which means if the function is assigned some value at the point of discontinuity it cannot be made continuous.

How signum function is expressed in terms of unit step function?

Explanation: The signum function is defined by. sgn(t)=⎧⎩⎨−1,0,1,t<0t=0t>0. Using the half-maximum convention, the unit step function is defined by. u(t)=⎧⎩⎨⎪⎪0,12,1,t<0t=0t>0.