What is Discrete time unit impulse?

A discrete-time unit impulse, often denoted as δ[n], is a sequence defined such that δ[n] = 1 when n = 0 and δ[n] = 0 for all other integer values of n. It serves as a fundamental building block in digital signal processing and systems analysis, representing an idealized instantaneous signal. The unit impulse function is crucial for analyzing linear time-invariant (LTI) systems, as it can be used to derive system responses through convolution.