# 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

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

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

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

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

9. Is the above system, i.e y[n] = x2[n-2] time invariant?
a) Yes
b) No

10. Is the function y[2n] = x[2n] linear in nature?
a) Yes
b) No

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

15. Zero-input response is also known as ____________
a) zero-state response
b) Natural response
c) state-input response
d) Forced response

16. The general solution of natural response is of the form of _________
a) yh (n)= c1 Î»1n+c2Î»2n+⋯+cNÎ»Nn
b) yh (n)= c1 Î»1n+c2Î»2n+⋯+cNÎ»Nn
c) yh (n)= c1 Î»12+c2Î»22+⋯+cNÎ»N2
d) yh(n)= c1 Î»1n-c2Î»2n+⋯+cNÎ»Nn
Answer: yh (n)= c1 Î»1n+c2Î»2n+⋯+cNÎ»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

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

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

c) Subtractor

d) Multiplier

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

21. The Z^-1is known as __________

a) Delay block

c) Multiplier 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

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

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

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

a) True

b) False

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

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

a) True

b) 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