Digital Signal Processing

Pade Approximation Method

Question 1
Marks : +2 | -2
Pass Ratio : 100%
The minimization of ε involves the solution of a set of non-linear equations.
True
False
Explanation:
In general, h(n) is a non-linear function of the filter parameters and hence the minimization of ε involves the solution of a set of non-linear equations.
Question 2
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Pass Ratio : 100%
Which of the following filters will have an impulse response as shown in the below figure?
Butterworth filters
Type-I chebyshev filter
Type-II chebyshev filter
None of the mentioned
Explanation:
The diagram that is given in the question is the impulse response of Butterworth filter.
Question 3
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Pass Ratio : 100%
For how many values of the impulse response, a perfect match is present between h(n) and hd(n)?
L
M+N+1
2L-M-N-1
All of the mentioned
Explanation:
We obtain a perfect match between h(n) and the desired response hd(n) for the first L values of the impulse response and we also know that L=M+N+1.
Question 4
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Pass Ratio : 100%
Which of the following techniques of designing IIR filters do not involve the conversion of an analog filter into digital filter?
Bilinear transformation
Impulse invariance
Approximation of derivatives
None of the mentioned
Explanation:
Except for the impulse invariance method, the design techniques for IIR filters involve the conversion of an analog filter into a digital filter by some mapping from the s-plane to the z-plane.
Question 5
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Pass Ratio : 100%
What should be the upper limit of the solution to match h(n) perfectly to the desired response hd(n)?
L
L+1
L-1
L+2
Explanation:
If we select the upper limit as U=L-1, it is possible to match h(n) perfectly to the desired response hd(n) for 0 < n < M+N.
Question 6
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Using which of the following methods, a digital IIR filter can be directly designed?
Pade approximation
Least square design in time domain
Least square design in frequency domain
All of the mentioned
Explanation:
There are several methods for designing digital filters directly. The three techniques are Pade approximation and least square method, the specifications are given in the time domain and the design is carried in time domain. The other one is least squares technique in which the design is carried out in frequency domain.
Question 7
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Pass Ratio : 100%
Which of the following conditions are in the favor of Pade approximation method?
Desired system function is rational
Prior knowledge of the number of poles and zeros
Desired system function is rational & Prior knowledge of the number of poles and zeros
None of the mentioned
Explanation:
The Pade approximation method results in a perfect match to Hd(z) when the desired system function is rational and we have prior knowledge of the number of poles and zeros in the system.
Question 8
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Pass Ratio : 100%
The degree to which the design technique produces acceptable filter designs depends in part on the number of filter coefficients selected.
True
False
Explanation:
The degree to which the design technique produces acceptable filter designs depends in part on the number of filter coefficients selected. Since the design method matches hd(n) only up to the number of filter parameters, the more complex the filter, the better the approximation to hd(n).
Question 9
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Pass Ratio : 100%
According to this method of designing, the filter should have which of the following in large number?
Only poles
Both poles and zeros
Only zeros
None of the mentioned
Explanation:
The major limitation of Pade approximation method, namely, the resulting filter must contain a large number of poles and zeros.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
What is the number of parameters that a filter consists of?
M+N+1
M+N
M+N-1
M+N-2
Explanation:
The filter has L=M+N+1 parameters, namely, the coefficients {ak} and {bk}, which can be selected to minimize some error criterion.