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 H(z)=∑Mk=0bkz−k1+∑Nk=1akz−k.**a) True**

b) False

2. If a_{k} is the filter coefficient and āk represents the quantized coefficient with Δa_{k} as the quantization error, then which of the following equation is true?

a) āk = a_{k}.Δa_{k}

b) āk = a_{k}/Δa_{k}**c) āk = a _{k} + Δa_{k}**

d) None of the mentioned

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

a) ∏Nk=1(1+pkz−1)

b) ∏Nk=1(1+pkz−k)

c) ∏Nk=1(1−pkz−k)**d) ∏Nk=1(1−pkz−1)**

4. If p_{k} is the set of poles of H(z), then what is Δp_{k} that is the error resulting from the quantization of filter coefficients?

a) Pre-turbation**b) Perturbation**

c) Turbation

d) None of the mentioned

5. What is the expression for the perturbation error Δp_{i}?**a) ∑Nk=1∂pi∂akΔak**

b) ∑Nk=1piΔak

c) ∑Nk=1Δak

d) None of the mentioned

6. Which of the following is the expression for ∂pi∂ak?

a) −pN+ki∏nl=1pi−pl

b) pN−ki∏nl=1pi−pl**c) −pN−ki∏nl=1pi−pl**

d) None of the mentioned

7. If the poles are tightly clustered as they are in a narrow band filter, the lengths of |p_{i}-p_{l}| are large for the poles in the vicinity of p_{i}.

a) True**b) False**

8. Which of the following operation has to be done on the lengths of |p_{i}-p_{l}| in order to reduce the perturbation errors?**a) Maximize**

b) Equalize

c) Minimize

d) None of the mentioned

b) Zeros

c) Poles & Z

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) Poles & Zeros

d) None of the mentioned

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

a) ∏Nk=1(1+pkz−1)

b) ∏Nk=1(1+pkz−k)

c) ∏Nk=1(1−pkz−k)**d) ∏Nk=1(1−pkz−1)**