Which of the following is a recursive form of a non-recursive system described by the equation y(n)=\(\frac{1}{M+1} \sum_{k=0}^Mx(n-k)\)?

y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)+x(n-1-M)]

y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)+x(n-1+M)]

y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)-x(n-1+M)]

y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)-x(n-1-M)]

What is the output of the system represented by the following direct form?

y(n)=-a1y(n-1)-a2y(n-2)- b0x(n)-b1x(n-1)-b2x(n-2)

y(n)=-a1y(n-1)-a2y(n-2)+ b0x(n)+b1x(n-1)+b2x(n-2)

y(n)=a1y(n-1)+a2y(n-2)+ b0x(n)+b1x(n-1)+b2x(n-2)

Which of the following is the difference equation of a special case of FIR system?

y(n) = \(\sum_{k=0}^{M} b_k x(n-k)\)

y(n) = \(a_0y(n)-\sum_{k=1}^{N} a_k y(n-k)\)

y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)\)

Explore topic-wise MCQs in Digital Signal Processing Questions and Answers.

This section includes 7 Mcqs, each offering curated multiple-choice questions to sharpen your Digital Signal Processing Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.	Which of the following is a recursive form of a non-recursive system described by the equation y(n)=\(\frac{1}{M+1} \sum_{k=0}^Mx(n-k)\)?
A.	y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)+x(n-1-M)]
B.	y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)+x(n-1+M)]
C.	y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)-x(n-1+M)]
D.	y(n)=y(n-1)+\(\frac{1}{M+1}\)[x(n)-x(n-1-M)]
Answer» E.

Discussion

2.	An FIR system is also called as “recursive system”.
A.	True
B.	False
Answer» C.

Discussion

3.	The system represented by the following direct form structure is:
A.	General second order system
B.	Purely recursive system
C.	Partial recursive system
D.	FIR system
Answer» E.

Discussion

4.	What is the output of the system represented by the following direct form?
A.	y(n)=-a1y(n-1)-a2y(n-2)- b0x(n)-b1x(n-1)-b2x(n-2)
B.	y(n)=-a1y(n-1)-a2y(n-2)+b0x(n)
C.	y(n)=-a1y(n-1)-a2y(n-2)+ b0x(n)+b1x(n-1)+b2x(n-2)
D.	y(n)=a1y(n-1)+a2y(n-2)+ b0x(n)+b1x(n-1)+b2x(n-2)
Answer» D. y(n)=a1y(n-1)+a2y(n-2)+ b0x(n)+b1x(n-1)+b2x(n-2)

Discussion

5.	What is the system does the following direct form structure represents?
A.	FIR system
B.	Purely recursive system
C.	General second order system
D.	None of the mentioned
Answer» C. General second order system

Discussion

6.	Which of the following is the difference equation of a special case of FIR system?
A.	y(n) = \(\sum_{k=0}^{M} b_k x(n-k)\)
B.	y(n) = \(a_0y(n)-\sum_{k=1}^{N} a_k y(n-k)\)
C.	y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)\)
D.	None of the mentioned
Answer» B. y(n) = \(a_0y(n)-\sum_{k=1}^{N} a_k y(n-k)\)

Discussion

7.	To implement the linear time invariant recursive system described by the difference equation y(n)=\(-\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^M b_k x(n-k)\) in Direct form-I, how many number of delay elements and multipliers are required respectively?
A.	M+N+1, M+N
B.	M+N-1, M+N
C.	M+N, M+N+1
D.	None of the mentioned
Answer» D. None of the mentioned

Discussion

Explore topic-wise MCQs in Digital Signal Processing Questions and Answers.

Which of the following is a recursive form of a non-recursive system described by the equation y(n)=\(\frac{1}{M+1} \sum_{k=0}^Mx(n-k)\)?

An FIR system is also called as “recursive system”.

The system represented by the following direct form structure is:

What is the output of the system represented by the following direct form?

What is the system does the following direct form structure represents?

Which of the following is the difference equation of a special case of FIR system?

To implement the linear time invariant recursive system described by the difference equation y(n)=\(-\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^M b_k x(n-k)\) in Direct form-I, how many number of delay elements and multipliers are required respectively?