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(ωt + π/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)
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 x2
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 n3 , value at n = 3 is 81.
y(n) = 5 n3 , value at n = 3 is 135
y(n) = 6 n2 , value at n = 3 is 54
y(n) = n3 , 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)
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)
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