Digital Signal Processing

Quantization of Filter Coefficients

Question 1
Marks : +2 | -2
Pass Ratio : 100%
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?
āk = ak.Δak
āk = ak/Δak
āk = ak + Δak
None of the mentioned
Explanation:
The quantized coefficient āk can be related to the un-quantized coefficient ak by the relation
Question 2
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the equivalent representation of the denominator of the system function of a general IIR filter?
\\(\\prod_{k=1}^N (1+p_k z^{-1})\\)
\\(\\prod_{k=1}^N (1+p_k z^{-k})\\)
\\(\\prod_{k=1}^N (1-p_k z^{-k})\\)
\\(\\prod_{k=1}^N (1-p_k z^{-1})\\)
Explanation:
We know that the system function of a general IIR filter is given by the equation
Question 3
Marks : +2 | -2
Pass Ratio : 100%
What is the expression for the perturbation error Δpi?
\\(\\sum_{k=1}^N \\frac{∂p_i}{∂a_k} \\Delta a_k\\)
\\(\\sum_{k=1}^N p_i \\Delta a_k\\)
\\(\\sum_{k=1}^N \\Delta a_k\\)
None of the mentioned
Explanation:
The perturbation error Δpi can be expressed as
Question 4
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the expression for \\(\\frac{∂p_i}{∂a_k}\\)?
\\(\\frac{-p_i^{N+k}}{\\prod_{l=1}^n p_i-p_l}\\)
\\(\\frac{p_i^{N-k}}{\\prod_{l=1}^n p_i-p_l}\\)
\\(\\frac{-p_i^{N-k}}{\\prod_{l=1}^n p_i-p_l}\\)
None of the mentioned
Explanation:
The expression for \\(\\frac{∂p_i}{∂a_k}\\) is given as follows
Question 5
Marks : +2 | -2
Pass Ratio : 100%
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.
True
False
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.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
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?
Pre-turbation
Perturbation
Turbation
None of the mentioned
Explanation:
We know that &pmacr;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.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the equivalent representation of the denominator of the system function of a general IIR filter?
\\(\\prod_{k=1}^N (1+p_k z^{-1})\\)
\\(\\prod_{k=1}^N (1+p_k z^{-k})\\)
\\(\\prod_{k=1}^N (1-p_k z^{-k})\\)
\\(\\prod_{k=1}^N (1-p_k z^{-1})\\)
Explanation:
We know that the system function of a general IIR filter is given by the equation
Question 8
Marks : +2 | -2
Pass Ratio : 100%
The system function of a general IIR filter is given as H(z)=\\(\\frac{\\sum_{k=0}^M b_k z^{-k}}{1+\\sum_{k=1}^N a_k z^{-k}}\\).
True
False
Explanation:
If ak and bk are the filter coefficients, then the transfer function of a general IIR filter is given by the expression H(z)=\\(\\frac{\\sum_{k=0}^M b_k z^{-k}}{1+\\sum_{k=1}^N a_k z^{-k}}\\)
Question 9
Marks : +2 | -2
Pass Ratio : 100%
The sensitivity analysis made on the poles of a system results on which of the following of the IIR filters?
Poles
Zeros
Poles & Zeros
None of the mentioned
Explanation:
The sensitivity analysis made on the poles of a system results on the zeros of the IIR filters.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
Which of the following operation has to be done on the lengths of |pi-pl| in order to reduce the perturbation errors?
Maximize
Equalize
Minimize
None of the mentioned
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.