### Discrete Time Systems multiple choice questions

# Discrete Time Systems

1. Comment on the causality of the following discrete time system: y[n] = x[-n].

a) Causal

b) Non causal

c) Both Casual and Non casual

d) None of the mentioned**
Answer: Non causal**

2. Is the function y[n] = cos(x[n]) periodic or not?

a) True

b) False**
Answer: True**

3. Consider the system y[n] = 2x[n] + 5. Is the function linear?

a) Yes

b) No**
Answer: No**

4. If n tends to infinity, is the accumulator function an unstable one?

a) The function is marginally stable

b) The function is unstable

c) The function is stable

d) None of the mentioned**
Answer: The function is unstable**

5. Comment on the causality of the discrete time system: y[n] = x[n+3].

a) Causal

b) Non Causal

c) Anti Causal

d) None of the mentioned**
Answer: Anti Causal**

6.Comment on the time invariance of the following discrete system: y[n] = x[2n+4].

a) Time invariant

b) Time variant

c) Both Time variant and Time invariant

d) None of the mentioned**
Answer: Time variant**

7. How is a linear function described as?

a) Zero in Finite out

b) Zero in infinite out

c) Zero in zero out

d) Zero in Negative out**
Answer: Zero in zero out**

8. Is the system y[n] = x2[n-2] linear?

a) Yes

b) No**
Answer: No**

9. Is the above system, i.e y[n] = x2[n-2] time invariant?

a) Yes

b) No**
Answer: Yes**

10. Is the function y[2n] = x[2n] linear in nature?

a) Yes

b) No**
Answer: Yes**

**Read also: **Causality And Stability Of Discrete Time Systems

11. Forced Response is solution of difference equation when ____________

a) Input is zero

b) Input is given and initial conditions are zero

c) Natural Response

d) Input is given and initial conditions are non-zero**
Answer: Input is given and initial conditions are zero**

12. Zero-state response of the system is _____________

a) Response of the system when initial state of the system is zero

b) Response of the system due to input alone

c) Response of the system due to input alone when initial state of the system is zero

d) Response of the system due to input alone when initial state is neglected**
Answer: Response of the system due to input alone when initial state of the system is zero**

13. Forced response consists of _________

a) Homogenous solution and general solution

b) General solution alone

c) Homogenous solution and particular solution

d) Particular solution alone**
Answer: Homogenous solution and particular solution**

14. The response of any discrete time system can be decomposed as _____________

a) Total Response=Impulse+step

b) Total Response=Impulse+Ramp

c) Total Response=zero-output response

d) Total Response=zero-state response+zero-input response**
Answer: Total Response=zero-state**

15. Zero-input response is also known as ____________

a) zero-state response

b) Natural response

c) state-input response

d) Forced response**
Answer: Natural response**

16. The general solution of natural response is of the form of _________

a) y_{h} (n)= c_{1} Î»_{1}^{n}+c^{2}Î»^{2}^{n}+⋯+c_{N}Î»_{N}^{n}

b) y_{h} (n)= c_{1} Î»_{1}^{n}+c^{2}Î»^{2}^{n}+⋯+c_{N}Î»_{N}^{n}

c) y_{h} (n)= c_{1} Î»_{1}^{2}+c_{2}Î»_{2}^{2}+⋯+c_{N}Î»_{N}^{2}

d) y_{h}(n)= c_{1} Î»_{1}^{n}-c^{2}Î»^{2}^{n}+⋯+c_{N}Î»_{N}^{n}**Answer: y _{h} (n)= c_{1} Î»_{1}^{n}+c^{2}Î»^{2}^{n}+⋯+c_{N}Î»_{N}^{n }**

17. The output signal when a signal x(n)=(0,1,2,3) is processed through an ‘Identical’ system is?

a) (3,2,1,0)

b) (1,2,3,0)

c) (0,1,2,3)

d) None of the mentioned

**Answer: (0,1,2,3)**

18. If a signal x(n) is passed through a system to get an output signal of y(n)=x(n+1), then the signal is said to be ____________

a) Delayed

b) Advanced

c) No operation

d) None of the mentioned

**Answer: None of the mentioned**

19. If the output of the system is y(n)=∑nk=−∞x(y) with an input of x(n) then the system will work as ___________

a) Accumulator

b) Adder

c) Subtractor

d) Multiplier

**Answer: Accumulator**

20. What is the output y(n) when a signal x(n)=n*u(n)is passed through a accumulator system under the conditions that it is initially relaxed?

a) n2+n+12

b) n(n+1)2

c) n2+n+22

d) None of the mentioned

**Answer: n(n+1)2**

21. The Z^-1is known as __________

a) Delay block

b) Advance block

c) Multiplier block

d) Adder block

**Answer: Delay block**

22. The output signal when a signal x(n)=(0,1,2,3) is processed through an ‘Delay’ system is?

a) (3,2,1,0)

b) (1,2,3,0)

c) (0,1,2,3)

d) None of the mentioned

**Answer: (1,2,3,0)**

23. The system described by the input-output equation y(n)=nx(n)+bx3(n) is a __________

a) Static system

b) Dynamic system

c) Identical system

d) None of the mentioned

**Answer: Static system**

24. Whether the system described by the input-output equations y(n)=x(n)-x(n-1) a Time-variant system.

a) True

b) False

**Answer: False**

25. The system described by the input-output equations y(n)=x2(n) is a Non-linear system.

a) True

b) False

**Answer: True**

26. If the output of the system of the system at any ‘n’ depends only the present or the past values of the inputs then the system is said to be __________

a) Linear

b) Non-Linear

c) Causal

d) Non-causal

**Answer: Causal**

27. The system described by the input-output equations y(n)=x(-n) is a causal system.

a) True

b) False

**Answer: False**

28. If a system do not have a bounded output for bounded input, then the system is said to be __________

a) Causal

b) Non-causal

c) Stable

d) Non-stable

**Answer: Non-stable**

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