Question

Which one of the following is not a unit step function?

This question was posed to me by my college professor while I was bunking the class.

My question comes from Useful Signals topic in division Signals and Systems Basics of Signals and Systems

Answer 1

The unit step function is commonly defined as a function that is zero for all negative time values and one for all positive time values. In other words:

\[ u(t) = \begin{cases}

0, & t < 0 \\

1, & t \geq 0

\end{cases} \]

If you were given options, the one that *is not a unit step function* would be any function that doesn’t follow this definition—for instance, a function that has different values for \( t \geq 0 \) or is not constant in value after zero.

Without the options, here are examples of functions that would *not* be considered unit step functions:

1. **Ramp Function** (\( r(t) = t \) for \( t \geq 0 \)) – This function is not constant after zero; it linearly increases with time.

2. **Impulse Function** (\( \delta(t) \)) – This is zero everywhere except at \( t = 0 \), where it’s undefined but has an integral of one. It’s a different signal type.

3. **Sinusoidal or Periodic Functions** (e.g., \( \sin(t) \)) – These are oscillatory and do not remain constant as \( t \) increases.

So, if one of these types or something similar was listed among the options, it would *not* be a unit step function.