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

1. 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

View Answer

Explanation: An identical system is a system whose output is same as the input, that is it does not perform any operation on the input and transmits it.

2. 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

View Answer

Explanation: For example, the value of the output at the time n=0 is y(0)=x(1), that is the system is advanced by one unit.

3. If the output of the system is with an input of x(n) then the system will work as:

a) Accumulator

b) Adder

c) Subtractor

d) Multiplier

View Answer

Explanation: From the equation given, y(n)=x(n)+x(n-1)+x(n-2)+…. .This system calculates the running sum of all the past input values till the present time. So, it acts as an accumulator.

4. 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) (n^{2}+n+1)/2

b) (n(n+1))/2

c) (n^{2}+n+2)/2

d) None of the mentioned

View Answer

Explanation: Given that the system is initially relaxed, that is y(-1)=0

According to the equation of the accumulator,

a) Delay block

b) Advance block

c) Multiplier block

d) Adder block

View Answer

Explanation: If the function to this block is x(n) then the output from the block will be x(n-1). So, the block is called as delay block or delay element.

6. 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

View Answer

Explanation: An delay system is a system whose output is same as the input, but after a delay.

7. The system described by the input-output equation y(n)=nx(n)+bx^{3}(n) is a:

a) Static system

b) Dynamic system

c) Identical system

d) None of the mentioned

View Answer

Explanation: Since the output of the system y(n) depends only on the present value of the input x(n) but not on the past or the future values of the input, the system is called as static or memory-less system.

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

a) True

b) False

View Answer

Explanation: If the input is delayed by k units then the output will be y(n,k)=x(n-k)-x(n-k-1)

If the output is delayed by k units then y(n-k)=x(n-k)-x((n-k)-1)

=>y(n,k)=y(n-k). Hence the system is time-invariant.

9. The system described by the input-output equations y(n)=x^{2}(n) is a Non-linear system.

a) True

b) False

View Answer

Explanation: Given equation is y(n)=x

^{2}(n)

Let y

_{1}(n)=x

_{1}

^{2}(n) and y

_{2}(n)=x

_{2}

^{2}(n)

y

_{3}(n)=y

_{1}(n)+y

_{2}(n)= x

_{1}

^{2}(n)+ x

_{2}

^{2}(n)≠(x

_{1}(n)+x

_{2}(n))

^{2}

So the system is non-linear.

a) Linear

b) Non-Linear

c) Causal

d) Non-causal

View Answer

Explanation: A system is said to be causal if the output of the system is defined as the function shown below

y(n)=F[x(n),x(n-1),x(n-2),…] So, according to the conditions given in the question, the system is a causal system.

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

a) True

b) False

View Answer

Explanation: For n=-1, y(-1)=x(1)

That is, the output of the system at n=-1 is depending on the future value of the input at n=1. So the system is a non-causal system.

12. 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

View Answer

Explanation: An arbitrary relaxed system is said to be BIBO stable if it has a bounded output for every value in the bounded input. So, the system given in the question is a Non-stable system.

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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