Question

Determine the value of the summation: ∑^∞n= -∞δ(n-1)sin2n.

(a) 1

(b) 0

(c) sin2

(d) sin4

The question was asked in quiz.

My question is taken from Discrete Time Signals in portion Signals and Systems Basics of Signals and Systems

Answer 1

Right answer is (c) sin2

The best explanation: ∑^∞n= -∞δ(n-1)sin2n

⇒ We know, δ(n) is impulse function which means δ(n)=1 when n=0

⇒ δ(n-1)=1 when n=1 otherwise it is 0.

Therefore, the summation’s limit reduces to n=1

⇒ ∑^∞n= -∞δ(n-1)sin2n = sin2n|n=1 = sin2.