Question

Which of the following is not true about unit impulse function?

This question was posed to me during an online interview.

The above asked question is from Elementary Signals in chapter Signals and Systems Basics of Signals and Systems

Answer 1

The following statements are generally used to describe the unit impulse function. Any statement deviating from these could be considered "not true" about the unit impulse function:

1. **It has an infinitely high amplitude at \( t = 0 \)** (in continuous-time) or at \( n = 0 \) (in discrete-time).

2. **Its integral over all time equals 1** in continuous-time; for discrete-time, its sum over all samples equals 1.

3. **It is used as an identity in convolution**—convolution of any signal with a unit impulse yields the original signal.

A statement that would be *false* might be one that claims:

- "The unit impulse function has a finite amplitude." (False, because it has an infinite amplitude in continuous time.)

  

Or:

- "The unit impulse has a value of 1 at every point in time." (False, as it is zero everywhere except at \( t = 0 \) in continuous-time or \( n = 0 \) in discrete-time.)