13.13. Example 4: Discrete-Time Convolution

Try these first

1. 1.

   Calculate (f ∗ g)[0] if f[n] = {2, 0} and g[n] = {1, 1}.

   Hint

   Look at the first elements of both sequences.

2. 2.

   What is the value of (f ∗ g)[1] if f[n] = {1, 2} and g[n] = {1, 1}?

   Hint

   Sum the products of overlapping indices.

3. 3.

   What is the convolution of f[n] = {1, 2, 1} and g[n] = {1, 1} at n=0?

   • 2
   • 1
   • 3
   • 0

   Hint

   Check the first elements of both sequences.

4. 4.

   True or False: The result of (f ∗ g)[0] will always equal f[0]*g[0] in discrete convolution.

   • True
   • False

   Hint

   Remember the basic definition of convolution at the start.

5. 5.

   Given f[n] = {2, 1} and g[n] = {1, 3}, find (f ∗ g)[n] for all indices.

   Hint

   Add contributions for each n index.

6. 6.

   In a digital system, how does the outcome of (f ∗ g)[2] change if g[n] has a delay? Provide a scenario.

   Hint

   Think about how delays affect signal timing.