Question

Choose the correct equation for finding the output of a discrete time convolution?

(a) y[n] = ∑x[k]h[n-k], k from 0 to ∞

(b) y[n] = ∑x[k]h[n-k], k from -∞ to  +∞

(c) y[n] = ∑x[k]h[k], k from 0 to ∞

(d) y[n] = ∑x[k]h[n], k from -∞ to  +∞

I had been asked this question in an internship interview.

My doubt is from Discrete Time Convolution in chapter Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

The correct option is (b) y[n] = ∑x[k]h[n-k], k from -∞ to  +∞

Easiest explanation: y[n]=∑x[k]h[n-k], k from -∞ to  +∞

Is the correct equation, where x[n] is the input and h[n] is the impulse response of the ∂[n] input of an LTI system. This is referred to as the convolution sum.