This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Discrete Time Signals”.

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

a) Periodic

b) Aperiodic

View Answer

Explanation: ‘y’ will be periodic only if x attains the same value after some time, T. However, if x is a one-one discrete function, it may not be possible for some x[n].

2. What is the time period of the function x[n] = exp(jwn)?

a) pi/2w

b) pi/w

c) 2pi/w

d) 4pi/w

View Answer

Explanation: Using Euler’s rule, exp(2pi*n) = 1 for all integer n. Thus, the answer can be derived.

3. What is the nature of the following function: y[n] = y[n-1] + x[n]?

a) Integrator

b) Differentiator

c) Subtractor

d) Accumulator

View Answer

Explanation: If the above recursive definition is repeated for all n, starting from 1,2.. then y[n] will be the sum of all x[n] ranging from 1 to n, making it an accumulator system.

a) Causal

b) Non Causal

View Answer

Explanation: As the value of the function depends solely on the value of the input at a time presently and/or in the past, it is a causal system.

5. Is the function y[n] = x[n-1] – x[n-4] memoryless?

a) The system doesn’t need to have memory

b) The system needs to have memory

View Answer

Explanation: Since the function needs to store what it was at a time 4 units and 1 unit before the present time, it needs memory.

6. Is the function y[n] = x[n-1] – x[n-56] causal?

a) The system is non causal

b) The system is causal

View Answer

Explanation: As the value of the function depends solely on the value of the input at a time presently and/or in the past, it is a causal system.

7. Is the function y[n] = y[n-1] + x[n] stable in nature?

a) It is stable

b) It is unstable

View Answer

Explanation: It is BIBO stable in nature, i.e. bounded input-bounded output stable.

8. If n tends to infinity, is the accumulator function a stable one?

a) The function is marginally stable

b) The function is stable

c) The function is unstable

View Answer

Explanation: The system would be unstable, as the output will grow out of bound at the maximally worst possible case.

a) Yes

b) No

View Answer

Explanation: As we take the sum of y[n], terms cancel out and deem z[n] to be BIBO stable.

10. We define y[n] = nx[n] – (n-1)x[n]. Now, z[n] = z[n-1] + y[n]. Is z[n] a causal system?

a) No

b) Yes

View Answer

Explanation: As the value of the function depends solely on the value of the input at a time presently and/or in the past, it is a causal system.

**Sanfoundry Global Education & Learning Series – Signals and Systems.**

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