Digital Signal Processing

Implementation of Discrete Time Systems

Question 1
Marks : +2 | -2
Pass Ratio : 100%
What is the form of the FIR system to compute the moving average of the signal x(n)?
y(n)=\\(\\frac{1}{M+1} \\sum_{k=0}^M x(n-k)\\)
y(n)=\\(\\frac{1}{M+1} \\sum_{k=0}^M x(n+k)\\)
y(n)=\\(\\frac{1}{M+1} \\sum_{k=0}^{\\infty} x(n-k)\\)
None of the mentioned
Explanation:
A normal FIR non-recursive system with the impulse response h(n)=\\(\\frac{1}{M+1}\\) is the system which is used to compute the moving average of a signal x(n).
Question 2
Marks : +2 | -2
Pass Ratio : 100%
The system represented by the following direct form structure is:
General second order system
Purely recursive system
Partial recursive system
FIR system
Explanation:
The output of the system according to the direct form given is
Question 3
Marks : +2 | -2
Pass Ratio : 100%
An FIR system is also called as “recursive system”.
True
False
Explanation:
For a system to be recursive, the output of the system must be dependent only on the past values of the output. For an FIR system the output of the system must be depending only on the present and past values of the input. So, FIR system is not an recursive system.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
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)\\)
None of the mentioned
Explanation:
If the coefficients of the past values of the output in the difference equation of the system, then the system is said to be FIR system.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
What is the system does the following direct form structure represents?
FIR system
Purely recursive system
General second order system
None of the mentioned
Explanation:
Since the output of the system depends only on the present value of the input and the past values of the output, the system is a purely recursive system.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
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)
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)
Explanation:
The equation of the difference equation of any system is defined as
Question 7
Marks : +2 | -2
Pass Ratio : 100%
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)]
Explanation:
The given system equation is y(n)=\\(\\frac{1}{M+1} \\sum_{k=0}^M x(n-k)\\)
Question 8
Marks : +2 | -2
Pass Ratio : 100%
Which of the following linear time invariant system is a purely recursive system?
y(n) = \\(-\\sum_{k=1}^{N} a_k y(n-k)+\\sum_{k=0}^{M} b_k x(n-k)\\)
y(n) = \\(\\sum_{k=1}^{N} a_k y(n-k)+\\sum_{k=0}^{M} b_k x(n-k)\\)
y(n) = \\(-\\sum_{k=1}^{N} a_k y(n-k)-\\sum_{k=0}^{M} b_k x(n-k)\\)
y(n) = \\(-\\sum_{k=1}^{N} a_k y(n-k)+b_0x(n)\\)
Explanation:
Since the output of the system depend only on the past values of output and the present value of the input, the system is called as “purely recursive” system.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
The system described by the equation y(n)=ay(n-1)+b x(n) is a recursive system.
True
False
Explanation:
Since the present output depends on the value of the previous output, the system is called a Recursive system.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
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?
M+N+1, M+N
M+N-1, M+N
M+N, M+N+1
None of the mentioned
Explanation:
From the given equation, there are M+N delays, so it requires M+N number of delay elements and it has to perform M+N+1 multiplications, so it require that many number of multipliers.