Question

2.
The relation between a signum function and unit step function is sign(t) =?
a) 2u(t)-1
b) u(t)
c) u(t)-1
d) u(t)-u(-1)​

Answer 1

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

From these two definitions it should be obvious that

sgn(t)=2u(t)−1

must hold.

Answer 2

The correct answer is option (a) 2 u(t) - 1

The signum function is defined by

                                  −1         t<0

                 sgn(t) = ⎨0           t=0

                               ⎨1            t>0

Using the half-maximum convention, the unit step function is defined by

                  u(t) = ⎧0,           t<0

                            ⎨1 / 2,       t=0

                            ⎩1,             t>0

From these two definitions it should be obvious that

                       sgn(t)=2u(t)−1

must hold.

• In arithmetic, the sign function or signum function (from signum, Latin for "sign") is an odd numerical function that removes the indication of a real number.
• To stay away from disarray with the sine function, this function is typically called the signum function.
• The Heaviside step function, or the unit step function, for the most part, meant by H or θ (yet at times u, 1 or ), is a stage function, named after Oliver Heaviside (1850-1925), the worth of which is zero for negative contentions and one for positive contentions.