Quiz 1 a

Find the response y[n] of the system.

h2[n] h1[n] y[n] h3[n]x[n]

1

0

h1[n] h1[n]

1/2

0

h1[n] h2[n]1/2

0

h1[n] h3[n]

2

4

22

0

x[n]

-2

2

Quiz 1 b

Find the response y[n] of the system.

h2[n] h1[n] y[n] h3[n]x[n]

0

h1[n] h1[n]

1/2

0

h1[n] h2[n]1/2

0

h1[n] h3[n]

2

4

22

0

x[n]

-2

1

Quiz 1 c

Find the response y[n] of the system.

h2[n] h1[n] y[n] h3[n]x[n]

0

h1[n] h1[n]

1/2

0

h1[n] h2[n]1/2

0

h1[n] h3[n]

2

22

0

x[n]

-2

1

-2

Quiz 1 Solution The three LTI systems are arranged in a cascade. A simple method of solving the problem is to find the impulse response due to h1[n] and h2[n] (call it h4[n]). Then find the response by convolving h4[n] and h3[n] (call it h5[n]) Convolve x[n] with h5[n] to get the answer. Let h4[n] = h1[n] * h2[n] and h5[n] = h4[n] * h3[n] while y[n] = x[n] * h5[n] Quiz 1a Solution h4[n] = [0 0.5 0.5] h5[n] = [0 1 1] y[n] = [0 2 4 6 2 0 2 0] Quiz 1b Solution h4[n] = [0 0 0.5 0.5] h5[n] = [0 0 1 1] y[n] = [0 0 2 2 4 2 0 2] Quiz 1c Solution h4[n] = [0 0 0 0.5 0.5] h5[n] = [0 0 0 1 1] y[n] = [0 0 0 2 2 -2 -4 0 2]