Question

What is a convolution sum?

(a) ∑x[k]h[n-k], k from -∞ to  +∞

(b) ∑x[k]*∑h[n-k], k from -∞ to  +∞

(c) ∑x[k]+∑h[n-k], k from -∞ to  +∞

(d) ∑∑x[k]h[n-k], k from -∞ to  +∞

I have been asked this question in exam.

Origin of the question is Discrete Time Convolution in division Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

Correct choice is (a) ∑x[k]h[n-k], k from -∞ to  +∞

Explanation: y[n]=∑x[k]h[n-k], k from -∞ to  +∞, y[n] is the output of the summation of the components on the right hand side. Where x[n] is the input of an LTI system and h[n] is the impulse response of the ∂[n] input of an LTI system. The response is due to superposition, in short.