Question

Discrete-time version of unit impulse is defined as ______

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Answer 1

The discrete-time version of the unit impulse is defined as the *Kronecker delta function*, denoted as \( \delta[n] \). It is defined by:

\[

\delta[n] =

\begin{cases}

1, & \text{if } n = 0 \\

0, & \text{if } n \neq 0

\end{cases}

\]

In other words, it’s a sequence that is zero everywhere except at \( n = 0 \), where it takes the value of 1. This function serves as the discrete counterpart to the Dirac delta function in continuous time. It is often used to analyze and characterize systems in discrete-time signal processing.