Question

The condition for memory-less system is given by _____

(a) h[k] = cδ[k]

(b) h[k] = cδ[n-k]

(c) h[k] = ch[k]δ[k]

(d) h[k] = ch[n-k]δ[k]

The question was posed to me in an interview for internship.

The above asked question is from Properties of the Impulse Response Representation for LTI Systems in portion Time Domain Representation for LTI Systems of Signals and Systems

Answer 1

The correct choice is (a) h[k] = cδ[k]

To elaborate: The LTI discrete-time system is said to be memory-less if and only if it satisfies the condition h[k]=cδ[k].  All memory-less LTI systems perform scalar multiplication on the input.