Test: Optimum Equiripple Filter Design - 2

# Test: Optimum Equiripple Filter Design - 2

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## 10 Questions MCQ Test Signals and Systems | Test: Optimum Equiripple Filter Design - 2

Test: Optimum Equiripple Filter Design - 2 for Electrical Engineering (EE) 2022 is part of Signals and Systems preparation. The Test: Optimum Equiripple Filter Design - 2 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Optimum Equiripple Filter Design - 2 MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Optimum Equiripple Filter Design - 2 below.
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Test: Optimum Equiripple Filter Design - 2 - Question 1

### If the filter has symmetric unit sample response with M odd, then what is the value of Q(ω)?

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 1

Explanation: If the filter has a symmetric unit sample response, then we know that
h(n)=h(M-1-n)
and for M odd in this case, Q(ω)=1.

Test: Optimum Equiripple Filter Design - 2 - Question 2

### If the filter has anti-symmetric unit sample response with M odd, then what is the value of Q(ω)?

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 2

Explanation: If the filter has a anti-symmetric unit sample response, then we know that
h(n)= -h(M-1-n)
and for M odd in this case, Q(ω)=sin(ω).

Test: Optimum Equiripple Filter Design - 2 - Question 3

### In which of the following way the real valued desired frequency response is defined?

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 3

Explanation: The real valued desired frequency response Hdr(ω) is simply defined to be unity in the pass band and zero in the stop band.

Test: Optimum Equiripple Filter Design - 2 - Question 4

The error function E(ω) should exhibit at least how many extremal frequencies in S?

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 4

Explanation: According to Alternation theorem, a necessary and sufficient condition for Pω) to be unique, best weighted chebyshev approximation, is that the error function E(ω) must exhibit at least L+2 extremal frequencies in S.

Test: Optimum Equiripple Filter Design - 2 - Question 5

The filter designs that contain maximum number of alternations are called as:

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 5

Explanation: In general, the filter designs that contain maximum number of alternations or ripples are called as maximal ripple filters.

Test: Optimum Equiripple Filter Design - 2 - Question 6

Remez exchange algorithm is an iterative algorithm used in error approximation.

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 6

Explanation: Initially, we neither know the set of external frequencies nor the parameters. To solve for the parameters, we use an iterative algorithm called the Remez exchange algorithm, in which we begin by guessing at the set of extremal frequencies.

Test: Optimum Equiripple Filter Design - 2 - Question 7

When |E(ω)|≤δ for all frequencies on the dense set, the optimal solution has been found in terms of the polynomial H(ω).

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 7

Explanation: |E(ω)|≥δ for some frequencies on the dense set, then a new set of frequencies corresponding to the L+2 largest peaks of |E(ω)| are selected and computation is repeated. Since the new set of L+2 extremal frequencies are selected to increase in each iteration until it converges to the upper bound, this implies that when |E(ω)|≤δ for all frequencies on the dense set, the optimal solution has been found in terms of the polynomial H(ω).

Test: Optimum Equiripple Filter Design - 2 - Question 8

In Parks-McClellan program, an array of maximum size 10 that specifies the weight function in each band is denoted by?

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 8

Explanation: FX denotes an array of maximum size 10 that specifies the weight function in each band.

Test: Optimum Equiripple Filter Design - 2 - Question 9

The filter designs which are formulated using chebyshev approximating problem have ripples in?

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 9

Explanation: The chebyshev approximation problem is viewed as an optimum design criterion on the sense that the weighted approximation error between the desired frequency response and the actual frequency response is spread evenly across the pass band and evenly across the stop band of the filter minimizing the maximum error. The resulting filter designs have ripples in both pass band and stop band.

Test: Optimum Equiripple Filter Design - 2 - Question 10

If the filter has symmetric unit sample response with M even, then what is the value of Q(ω)?

Detailed Solution for Test: Optimum Equiripple Filter Design - 2 - Question 10

Explanation: If the filter has a symmetric unit sample response, then we know that
h(n)=h(M-1-n)
and for M even in this case, Q(ω)= cos(ω/2).

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## Signals and Systems

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