Question

What is the sum of impulses in a convolution sum of two discrete time sequences?

(a) Sy = SxSh, Sx=∑x(k) and Sh = ∑h(n-k)

(b) Sy = Sx+Sh, Sx=∑x(k-1) and Sh = ∑h(n-k)

(c) Sy = Sx-Sh, Sx=∑x(k) and Sh = ∑h(n-k)

(d) Sy = Sx*Sh, Sx=∑x(n) and Sh = ∑h(n-k)

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

This interesting question is from Discrete Time Convolution in chapter Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

The correct option is (a) Sy = SxSh, Sx=∑x(k) and Sh = ∑h(n-k)

For explanation: Sy=Sx+Sh, , Sx = ∑x(k) and Sh = ∑h(n-k),  the sum of impulses in a convolution sum of two discrete time sequences is the product of the sums of the impulses in the two individual sequences. Here, y(n)=x(n)*h(n).