This set of Signals & Systems test focuses on “Properties of Systems – 4”.

1. What is a stable system?

a) If every bounded input results in the bounded output

b) If every bounded input results in an unbounded output

c) If every unbounded input results in a bounded output

d) If unbounded input results in bounded as well as unbounded output

View Answer

Explanation: The system is said to bounded input bounded output stable if every bounded input results in bounded output and also the output of such a system does not diverge if the input does not diverge.

2. If This is an example for _______ system.

a) Stable system

b) Unstable system

c) Bounded input unbounded output system

d) Unbounded input system

View Answer

Explanation: In the above example, the input is finite and the output is also finite as y (t) is absolute integrable. Hence the system is stable.

3. If x(t)= ∂(t-1) and y(t)= e^{-t}. This is an example for ______ system.

a) Stable

b) BIBO

c) Bounded input

d) Unstable

View Answer

Explanation: In this example, the input is finite and output is not finite. Hence the given system is unstable.

3. If x(t)=e^{t}, y(t)= e^{-2t} this is a _____system.

a) Unstable

b) Stable

c) BIBO

d) Cannot classify the system

View Answer

Explanation: In this example, the input is infinite and hence this input cannot be used to classify the system. Here the output is not considered.

4. Which of the following is not true about systems having memory?

a) It is also called dynamic systems

b) The output signal depends on the past values of the input signal

c) It is also called static system

d) Resistive circuit

View Answer

Explanation: The system is said to have memory if its output signal depends on the past values of the input signal and also it is called dynamic system.

5. How far does the memory of the given system y[n]=1/2{x[n]+ x[n-1]} extend into past?

a) Two time units

b) One time unit

c) Three time units

d) Not predictable

View Answer

Explanation: The given memory system extends into past by one time unit. It is determined by the term x [n-1].

6. The input- output relation of a device is represented asi(t)=ao+a1v1(t)+a2v^{2} (t)+⋯. Does this device have memory?

a) Has memory

b) Does not have memory

c) It is dynamic

d) Insufficient information

View Answer

Explanation: In the given equation, v (t) is the voltage applied I (t) is the current flowing through the device and a0, a1, a2 are the constants. It does not involve any past value of the input signal and hence memory less.

7. Which is not an example for memory system?

a) Capacitive circuit

b) Inductive circuit

c) Resistive circuit

d) Parallel RC circuit

View Answer

Explanation: Resistive circuit is memory less since the current I (t) flowing through it in response to the applied voltage v (t) is defined by i(t) =

^{1}⁄

_{R}v(t).

8. What is the memory of the system if its input-output relation is given by ?

a) Memory extends from time t to the infinite future

b) Memory extends from time t to the infinite past

c) Does not have memory

d) Insufficient information

View Answer

Explanation: Given system has inductor involved in it. Hence it has memory. Since integral is from -∞ to time t, its memory extends from time t to infinite past.

9. Which of the following systems is memory less?

a) y(t) = 2x(t) + ^{d}⁄_{dx} x(t)

b) y(t) = 2x^{2} (t) + ^{d}⁄_{dx} x(t)

c) y(t) = ∫x(t)dt

d) y(t) = 2x^{2} (t)

View Answer

Explanation: A differentiator or integrator maybe realized with capacitors and inductors and cannot be realized using resistors. Hence differentiators and integrators can be considered as systems with memory.

10. An example for non-causal system is ________

a) Amplifier

b) Oscillator

c) Rectifiers

d) Does not exists

View Answer

Explanation: Non-causal system is the one which results in output even without the application of input. Since all systems are real, non-causal systems do not exists.

11. Is Ideal low pass filter is an example for Non –causal system?

a) True

b) False

View Answer

Explanation: Ideal low pass filter has sharp transitions which cannot be physically realized. Hence non – causal.

12. Can impulse response be measured?

a) Impulse cannot be generated

b) Impulse can be generated

c) Can be measured

d) Cannot be measured

View Answer

Explanation: Impulse response can be measured but in an indirect manner. Hence by giving step response to a suitable differentiator impulse response is measured. Impulse response is derivative of step response.

13. Which of the following is an example for non- causal system?

a) y[n] = ^{1}⁄_{3} {x[n-1] + x[n] + x[n-2]}

b) y[n] = ^{1}⁄_{3} {x[n-1] + x[n] + x[n+1]}

c) y[n] = ^{1}⁄_{2} {x[n-1] + x[n]}

d) y[n] = ^{1}⁄_{2} {x[n] + x[n-2]}

View Answer

Explanation: y[n] =

^{1}⁄

_{3}{x[n-1] + x[n] + x[n+1]} is an example for non- causal system since the output y [n] depends on the future value of the input namely x [n+1].

14. Which of the following is not true about invertible systems?

a) H^{-1} H=I

b) There must be one-to-one mapping between input and output signals for a system to be invertible

c) Input of the invertible system can be recovered from the system output

d) Input of the invertible system cannot be recovered from the system output

View Answer

Explanation: By the definition of invertible system we can say that input of the invertible system can be recovered from the system output.

15. Is y(t)= x^{2} (t) is an example for invertible system?

a) True

b) False

View Answer

Explanation: In this example we don’t have a unique inverse hence the input of the system is not recovered from the system output. Hence it is considered as non-invertible system.

16. y(t) = 2x(t) + 3t ^{d}⁄_{dx} x(t) Is an example for _____

a) Time invariant system

b) Time varying system

c) LTI system

d) Time invariant and linear system

View Answer

Explanation: The given system does not satisfy the condition {R{x(t-to)}=y(t-to)} hence the system is time varying.

17. y(t) = 5x(t) + 6 ^{d}⁄_{dx} x(t) Is an example for _____ system.

a) Time varying

b) Time invariant

c) Time varying and linear

d) Time varying and non linear

View Answer

Explanation: The given system satisfies the condition {R{x(t-to)}=y(t-to)} hence the system is time invariant.

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