Digital Signal Processing

Structures for Realization of Discrete Time Systems

Question 1
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the rational system function of an LTI system characterized by the difference equation y(n)=-\\(\\sum_{k=1}^N a_k y(n-k)+\\sum_{k=0}^N b_k x(n-k)\\)?
\\(\\frac{\\sum_{k=0}^N b_k x(n-k)}{1+\\sum_{k=0}^N a_k y(n-k)}\\)
\\(\\frac{1+\\sum_{k=1}^N a_k y(n-k)}{\\sum_{k=0}^N b_k x(n-k)}\\)
\\(\\frac{\\sum_{k=0}^N b_k x(n-k)}{1+\\sum_{k=1}^N a_k y(n-k)}\\)
\\(\\frac{1+\\sum_{k=0}^N a_k y(n-k)}{\\sum_{k=0}^N b_k x(n-k)}\\)
Explanation:
The difference equation of the LTI system is given as
Question 2
Marks : +2 | -2
Pass Ratio : 100%
Which of the following refers the number of memory locations required to store the system parameters, past inputs, past outputs and any intermediate computed values?
Computational complexity
Finite world length effect
Memory requirements
None of the mentioned
Explanation:
Memory requirements refers the number of memory locations required to store the system parameters, past inputs, past outputs and any intermediate computed values.
Question 3
Marks : +2 | -2
Pass Ratio : 100%
Finite word length effects refer to the quantization effects that are inherent in any digital implementation of the system, either in hardware or software.
True
False
Explanation:
The parameters of the system must necessarily be represented with finite precision. The computations that are performed in the process of computing an output from the system must be rounded off or truncated to fit within the limited precision constraints of the computer or hardware used in the implementation. Thus, Finite word length effects refer to the quantization effects that are inherent in any digital implementation of the system, either in hardware or software.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
The general linear constant coefficient difference equation characterizing an LTI discrete time system is?
y(n)=-\\(\\sum_{k=1}^N a_k y(n-k)+\\sum_{k=0}^N b_k x(n-k)\\)
y(n)=-\\(\\sum_{k=0}^N a_k y(n-k)+\\sum_{k=0}^N b_k x(n-k) \\)
y(n)=-\\(\\sum_{k=1}^N a_k y(n)+\\sum_{k=0}^N b_k x(n) \\)
None of the mentioned
Explanation:
We know that, the general linear constant coefficient difference equation characterizing an LTI discrete time system is given by the expression
Question 5
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is used in the realization of a system?
Delay elements
Multipliers
Adders
All of the mentioned
Explanation:
From each set of equations, we can construct a block diagram consisting of an interconnection of delay elements, multipliers and adders.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
Which of the following are called as finite word length effects?
Parameters of the system must be represented with finite precision
Computations are truncated to fit in the limited precision constraints
Whether the computations are performed in fixed point or floating point arithmetic
All of the mentioned
Explanation:
All the three of the considerations given above are called as finite word length effects.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
The number of times a fetch from memory is performed per output sample is one of the factor used in the implementation of the system.
True
False
Explanation:
According to the recent developments in the design and fabrication of rather sophisticated programmable DSPs, other factors, such as the number of times a fetch from memory is performed or the number of times a comparison between two numbers is performed per output sample, have become important in assessing the computational complexity of a given realization of a system.
Question 8
Marks : +2 | -2
Pass Ratio : 100%
Computational complexity refers to the number of ____________
Additions
Arithmetic operations
Multiplications
None of the mentioned
Explanation:
Computational complexity is one of the factor which is used in the implementation of the system. It refers to the numbers of Arithmetic operations (Additions, multiplications and divisions).
Question 9
Marks : +2 | -2
Pass Ratio : 100%
We can view y(n)=-\\(\\sum_{k=1}^N a_k y(n-k)+\\sum_{k=0}^N b_k x(n-k)\\) as the computational procedure (an algorithm) for determining the output sequence y(n) of the system from the input sequence x(n).
True
False
Explanation:
The computations in the given equation can be arranged into equivalent sets of difference equations. Each set of equations defines a computational procedure or an algorithm for implementing the system.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
The factors Computational complexity, memory requirements and finite word length effects are the ONLY factors influencing our choice of the realization of the system.
True
False
Explanation:
Apart from the three factors given in the question, other factors such as, whether the structure or the realization lends itself to parallel processing or whether the computations can be pipelined are also the factors which influence our choice of the realization of the system.