Question

Find the convolution sum of two sequences x(n)={1,2,3} and h(n)={1,2,-2,-1}

Answer 1

'Ello mate

          'Ere it is for you,

then by time invariance we get our answer.

h(n − k) = L [δ(n − k)]

δ(n − k) −→ L −→ h(n − k)

This means that if we know one input-output pair for this system, namely

δ(n) −→ L −→ h(n)

then we can infer

x(n) −→ L −→ y(n)

which gives us the following.

y(n) = X∞

k=−∞

x(k)h(n − k)

This is the convolution sum for DT LTI systems.

The convolution sum for x(n) and h(n) is usually written as shown here.

y(n) = x(n) ∗ h(n) = X∞

k=−∞

x(k)h(n − k)

                                           Complicated indeed

                                                                      -Hope This Helps Mate-