This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Quantization of Filter Coefficients”.

1. The system function of a general IIR filter is given as

a) True

b) False

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

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?

a) a ̅k = ak. Δak

b) a ̅k = ak/Δak

c) a ̅k = ak + Δak

d) None of the mentioned

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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.

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

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

a) Pre-turbation

b) Perturbation

c) Turbation

d) None of the mentioned

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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.

5. What is the expression for the perturbation error Δpi?

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6. Which of the following is the expression for

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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.

a) True

b) False

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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.

a) Maximize

b) Equalize

c) Minimize

d) None of the mentioned

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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.

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

a) Poles

b) Zeros

c) Both of the mentioned

d) None of the mentioned

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

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

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

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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