**1. **(TCO 1) A signal that is a function of time has following properties or the following applies to it.(Points : 4) it is impossible to change the properties of a signal.

A signal can be modified by a system which applies a transformation to it.

an electrical signal can only be transformed into an electrical signal.

an electrical signal can only be transformed into a non-electrical signal.

** **

Question 2. **2. **(TCO 1) A sinusoidal signal, 4 sin(ωt), passing through an LTI system, undergoes a gain of 1.5 and a 45-degree phase lag. The resulting output signal will be mathematically described as(Points : 4) |
5.5 sin(ωt).
6 sin(ωt – π/4).
6 sin(ωt + π/4).
5.5 sin(ωt – π/4). |

Question 3. **3. **(TCO 1) Determine which of the following is a linear system by applying the principle of superposition. (Points : 4) |
y = x^{2}
y= 2 x + 2
y = 2x |

Question 4. **4. **(TCO 1) A continuous time system has an output, *y,* which is given by . It is sampled at a frequency of 2 Hz. Determine the expression that correctly represents the discrete signal obtained after sampling and its value for *n* = 2. (Points : 4) |
y(n) = , value at n = 2 is -1
y(n) = , value at n = 2 is 0.0174
y(n) = , value at n = 2 is 0
y(n) = , value at n = 2 is 0.841 |

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 15 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 continuous signal is described by 15 sin( 100t + pi/2).
Its numerical value at *t* = 0 seconds is given by (Points : 4) |
15.
pi/2.
100.
0. |

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) |
– 2δ(n-1) – 2 δ(n-2) + δ (n-3) +δ (n-4)
δ(n-1) – 2 δ(n-2) – 2 δ (n-3) – δ (n-4)
-2δ(n) – δ(n-1) – δ (n-2) + + δ(n-3)
δ(n-1) + 2 δ(n-2) + δ(n-3) +2 δ (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) -4 U(n-1) + 3 U(n-2)
2U(n) -4 U(n-1) + 3 U(n-2) – U(n-3)
-2U(n) +4 U(n-1) + 3 U(n-2) – 3U(n-3)
2U(n) + 4 U(n-1) + 3 U(n-2) – 3U(n-3) |

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