Signals & Systems Questions and Answers Part-4

1. Which of the following is an example of amplitude scaling?
a) Electronic amplifier
b) Electronic attenuator
c) Both amplifier and attenuator
d) Adder

Answer: c
Explanation: Amplitude scaling refers to multiplication of a constant with the given signal.
It is given by y (t) = a x (t). It can be both increase in amplitude or decrease in amplitude.

2. Resistor performs amplitude scaling when x (t) is voltage, a is resistance and y (t) is output current.
a) True
b) False

Answer: b
Explanation: The given statement is not true. The relation between voltage, current and resistance is given by V = IR. Comparing with equation y (t) = a x (t), we can see that y (t) is the output voltage for given current x (t) with resistance R.

3. Which of the following is an example of physical device which adds the signals?
a) Radio
b) Audio mixer
c) Frequency divider
d) Subtractor

Answer: b
Explanation: Audio mixer is a device which combines music and voice signals. It is given by Y (t) = x1 (t) + x2 (t).

4. AM radio signal is an example for __________
a) y (t) = a x (t)
b) y (t) = x1 (t) + x2 (t)
c) y (t) = x1 (t) * x2 (t)
d) y (t) = -x(t)

Answer: c
Explanation: AM radio signal is an example for y (t) = x1 (t) * x2 (t) where, x1 (t) consists of an audio signal plus a dc component and x2 (t) is a sinusoidal signal called carrier wave.

5. Which of the passive component performs differentiation operation?
a) Resistor
b) Capacitor
c) Inductor
d) Amplifier

Answer: c
Explanation: Inductor performs differentiation. It is given by y (t) = L d/dt i(t) where, I (t) denotes current flowing through an inductor of inductance L.

6. Which of the component performs integration operation?
a) Resistor
b) Diode
c) Capacitor
d) Inductor

Answer: c
Explanation: Capacitor performs integration. V (t) developed across capacitor is given by
v (t) = (1/C)* ∫t-∞ i (∂).d∂, I (t) is the current flowing through a capacitor of capacitance C.

7. Time scaling is an operation performed on _______
a) Dependent variable
b) Independent variable
c) Both dependent and independent variable
d) Neither dependent nor independent variable

Answer: b
Explanation: Time scaling is an example for operations performed on independent variable time.
It is given by y (t) = x (at).

8. Y (t) = x (2t) is ________
a) Compressed signal
b) Expanded signal
c) Shifted signal
d) Amplitude scaled signal by a factor of 2

Answer: a
Explanation: By comparing the given equation with y (t) = x (at) we get a=2. If a>1 then it is compressed version of x (t).

9. Y (t) = x (t/5) is _______
a) Compressed signal
b) Expanded signal
c) Time shifted signal
d) Amplitude scaled signal by factor 1/5

Answer: b
Explanation: y (t) = x (at), comparing this with the given expression we get a = 1/5. If 0<a<1 then it is expanded (stretched) version of x (t).

10. In discrete signal, if y [n] = x [k*n] and k>1 then ______
a) Some samples are lost from x [n]
b) Some samples are added to x [n]
c) It has no effect on samples
d) Samples will be increased with factor k

Answer: a
Explanation: For discrete time signal y [n] = x [k*n] and k>1, it will be compressed signal and some samples will be lost. The samples lost will not violate the rules of sampling theorem.