Digital Signal Processing Questions and Answers – Discrete Time Systems

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

Answer: c
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

Answer: d
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 \(y(n)=\sum_{k=-\infty}^nx(y)\) with an input of x(n) then the system will work as ___________
a) Accumulator
b) Adder
c) Subtractor
d) Multiplier
View Answer

Answer: a
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.
advertisement
advertisement

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) \(\frac{n^2+n+1}{2}\)
b) \(\frac{n(n+1)}{2}\)
c) \(\frac{n^2+n+2}{2}\)
d) None of the mentioned
View Answer

Answer: b
Explanation: Given that the system is initially relaxed, that is y(-1)=0
According to the equation of the accumulator,
y(n)=\(∑_{k=-∞}^n x(n)\)
=\(∑_{k=-∞}^{-1} x(n)+∑_{k=0}^n x(n)\)
=\(y(-1)+ ∑_{k=0}^n n*u(n)\)
=\(0+∑_{k=0}^n n\)(since u(n)=1 in 0 to n)
=\(\frac{n(n+1)}{2}\)

5. The block denoted as follows is known as __________
The block is delay block if function to block is x(n) then output from block is x(n-1)
a) Delay block
b) Advance block
c) Multiplier block
d) Adder block
View Answer

Answer: a
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.
Note: Join free Sanfoundry classes at Telegram or Youtube

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

Answer: b
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)+bx3(n) is a __________
a) Static system
b) Dynamic system
c) Identical system
d) None of the mentioned
View Answer

Answer: a
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.
advertisement

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

Answer: b
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)=x2(n) is a Non-linear system.
a) True
b) False
View Answer

Answer: a
Explanation: Given equation is y(n)=x2(n)
Let y1(n)=x12(n) and y2(n)=x22(n)
y3(n)=y1(n)+y2(n)= x12(n)+ x22(n)≠(x1(n)+x2(n))2
So the system is non-linear.
advertisement

10. 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
View Answer

Answer: c
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

Answer: b
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

Answer: d
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.

To practice all areas of Digital Signal Processing, here is complete set of 1000+ Multiple Choice Questions and Answers.

If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]

advertisement
advertisement
Subscribe to our Newsletters (Subject-wise). Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Youtube | Telegram | LinkedIn | Instagram | Facebook | Twitter | Pinterest
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

Subscribe to his free Masterclasses at Youtube & discussions at Telegram SanfoundryClasses.