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

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?

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.

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

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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