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University of Illinois at Chicago Department of Electrical and Computer Engineering ECE 317 Digital Signal Processing I Quiz No. 2 2/12/2020 Team Number: 1. Please find z[n] = x[n] ∗ y[n] for (1) x[n] = (2, 1, −1, −2) ⇑ n=0

(2). x[n] =

¡ 1 ¢n 2

u[n] and y[n] =

¡ 1 ¢n 3

y[n] = (1, 2, 2) ⇑ n=0

u[n].

University of Illinois at Chicago Department of Electrical and Computer Engineering ECE 317 Digital Signal Processing I Quiz No. 2 2/12/2020 Team Number:

3. A LTI system satisfies equation 1 1 y[n] + y[n − 1] − y[n − 2] = x[n] 6 6 (1). Determine the frequency response H(ejw ) of the system. (2). Determine the impulse response h[n] of the sytem. (3). Determine the output y[n] if the input is x[n] = (1/2)n u[n].

University of Illinois at Chicago Department of Electrical and Computer Engineering ECE 317 Digital Signal Processing I Quiz No. 2 2/12/2020 Team Number:

2. A LTI system has frequency response H(ejw ) =

1 . 1 + 21 e−j4w

Determine the output y[n] if the input x[n] is x[n] = cos(πn/4)....