Question

Convolve graphically the below given signals, and determine the correct sequence?

(a) Y (-1) = 0, y (1) = 2, y (3) = 2

(b) Y (-1) = 2, y (1) = 2, y (3) = 2

(c) Y (-1) = 0, y (1) = 0, y (3) = 2

(d) Y (-1) = 0, y (1) = 3, y (3) = 2

I got this question during an online exam.

Asked question is from Convolution : Impulse Response Representation for LTI Systems in division Time Domain Representation for LTI Systems of Signals and Systems

Answer 1

The correct choice is (a) Y (-1) = 0, y (1) = 2, y (3) = 2

The best I can explain: Step 1: sketch x (τ) and h (-τ)

Step 2: Obtain the product x (τ) h (t-τ) and the area under this product will give y (0)

Step 3: sketch h (1-τ) and compute y (1) and so on

Step 4: similarly sketch h (-1-τ) and compute y (-1) and so on.

By following above steps we get the output as