# Filter Coefficients Quantization

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 ak is the filter coefficient and āk represents the quantized coefficient with Δak as the quantization error, then which of the following equation is true?
a) āk = ak.Δak
b) āk = ak/Δak
c) āk = ak + Δak
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 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

5. What is the expression for the perturbation error Δpi?
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 |pi-pl| are large for the poles in the vicinity of pi.
a) True
b) False

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

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)