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Test: Filter Coefficients Quantization


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10 Questions MCQ Test Signals and Systems | Test: Filter Coefficients Quantization

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

The system function of a general IIR filter is given as  

Detailed Solution for Test: Filter Coefficients Quantization - Question 1

Explanation: If ak and bk are the filter coefficients, then the transfer function of a general IIR filter is given by the expression

Test: Filter Coefficients Quantization - Question 2

If ak is the filter coefficient and a ̅k represents the quantized coefficient with Δak as the quantization error, then which of the following equation is true?

Detailed Solution for Test: Filter Coefficients Quantization - Question 2

Explanation: The quantized coefficient a ̅k can be related to the un-quantized coefficient ak by the relation
a ̅k = ak + Δak
where Δak represents the quantization error.

Test: Filter Coefficients Quantization - Question 3

 

 Which of the following is the equivalent representation of the denominator of the system function of a general IIR filter?

Detailed Solution for Test: Filter Coefficients Quantization - Question 3

 

Explanation: We know that the system function of a general IIR filter is given by the equation

Test: Filter Coefficients Quantization - Question 4

 If pk is the set of poles of H(z), then what is Δpk that is the error resulting from the quantization of filter coefficients?

Detailed Solution for Test: Filter Coefficients Quantization - Question 4

Explanation: We know that p ̅k = pk + Δpk, k=1,2…N and Δpk that is the error resulting from the quantization of filter coefficients, which is called as perturbation error.

Test: Filter Coefficients Quantization - Question 5

What is the expression for the perturbation error Δpi?

Detailed Solution for Test: Filter Coefficients Quantization - Question 5

 

Explanation:

Test: Filter Coefficients Quantization - Question 6

Which of the following is the expression for

Detailed Solution for Test: Filter Coefficients Quantization - Question 6

Explanation:

Test: Filter Coefficients Quantization - Question 7

If the poles are tightly clustered as they are in a narrow band filter, the lengths of |pi-pl| are large for the poles in the vicinity of pi.

Detailed Solution for Test: Filter Coefficients Quantization - Question 7

Explanation: If the poles are tightly clustered as they are in a narrow band filter, the lengths of |pi-pl| are small for the poles in the vicinity of pi. These small lengths will contribute to large errors and hence a large perturbation error results.

Test: Filter Coefficients Quantization - Question 8

Which of the following operation has to be done on the lengths of |pi-pl| in order to reduce the perturbation errors?

Detailed Solution for Test: Filter Coefficients Quantization - Question 8

Explanation: The perturbation error can be minimized by maximizing the lengths of |pi-pl|. This can be accomplished by realizing the high order filter with either single pole or double pole filter sections.

Test: Filter Coefficients Quantization - Question 9

The sensitivity analysis made on the poles of a system results on which of the following of the IIR filters?

Detailed Solution for Test: Filter Coefficients Quantization - Question 9

Explanation: The sensitivity analysis made on the poles of a system results on the zeros of the IIR filters.

Test: Filter Coefficients Quantization - Question 10

Which of the following is the equivalent representation of the denominator of the system function of a general IIR filter?

Detailed Solution for Test: Filter Coefficients Quantization - Question 10

Explanation: We know that the system function of a general IIR filter is given by the equation

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