1. (TCO 1) A signal that is a function of time has the following properties (or the following applies to it). (Points : 4) It may originate from an electrical or a nonelectrical system (e.g., mechanical). It cannot be periodic. It must always be periodic. It must always be discrete and never analog or continuous. Question 2. 2. (TCO 1) A sinusoidal signal, 20 sin(?t + ?/2 ), passing through an LTI system, undergoes a gain of 2 and a 90-degree phase lag. The resulting output signal will be mathematically described as (Points : 4) 22 sin(?t + ?/2). 40 sin(?t ). 10 sin(?t + ?/2). 40 sin(?t – ?/2). Question 3. 3. (TCO 1) Determine which of the following is a linear system by applying the principle of superposition. (Points : 4) y = 0.5 x +0.5 y = 0.5 x -0.5 y = .5 x y = 0.5 x 2 Question 4. 4. (TCO 1) A continuous time system has an output, y, which is a function of time and is given by . It is sampled at a frequency of 1 Hz. Determine the expression that correctly represents the discrete signal obtained after sampling and its value for n = 3. (Points : 4) y(n) = 3 n 3 , value at n = 3 is 81. y(n) = 5 n 3 , value at n = 3 is 135 y(n) = 6 n 2 , value at n = 3 is 54 y(n) = n 3 , value at n = 3 is 27 Question 5. 5. (TCO 1) A signal given by 5 Cos (20*pi*t) + 20 Sin (40*pi*t) is sampled at a rate of 50 Hz. Is the Nyquist theorem violated? (Points : 4) No, it is not violated. Yes, it is violated. Insufficient data to answer the question Question cannot be answered because sampling time is unknown Question 6. 6. (TCO 1) A sawtooth wave repeats itself every 0.05 seconds. The first three harmonics in this sawtooth wave have a frequency of (Points : 4) 0.05, 0.1, 0.15 Hz. 40, 80, 120 Hz. 20, 40, 60 Hz. 50, 100, 150 Hz. Question 7. 7. (TCO 1) A discrete time sequence is shown below in a figure. All values not shown can be assumed to be zero. Describe the sequence as a sum of undelayed (if any) and delayed step functions. (Points : 3) – 2?(n-1) – 2 ?(n-2) + ? (n-3) +? (n-4) ?(n-1) – 2 ?(n-2) – 2 ? (n-3) – ? (n-4) -2?(n) –  ?(n-1) –  ? (n-2) +  + ?(n-3) ?(n-1) + 2 ?(n-2) + ?(n-3) +2 ? (n-4) Question 8. 8. (TCO 1) A discrete time sequence is shown below in a figure. All values not shown can be assumed to be zero. Describe the sequence as a sum of undelayed (if any) and delayed step functions. (Points : 3) 2U(n) -3 U(n-1) 2U(n-1) – 3U(n-2) 2U(n-1) -3 U(n-2) + U(n-3) 2U(n) +3 U(n-1) – U(n-3)

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