Digital Signal Processing

Design of FIR Filters

Question 1
Marks : +2 | -2
Pass Ratio : 50%
If H(z) is the z-transform of the impulse response of an FIR filter, then which of the following relation is true?
zM+1.H(z-1)=±H(z)
z-(M+1).H(z-1)=±H(z)
z(M-1).H(z-1)=±H(z)
z-(M-1).H(z-1)=±H(z)
Explanation:
We know that H(z)=\\(\\sum_{k=0}^{M-1} h(k)z^{-k}\\) and h(n)=±h(M-1-n) n=0,1,2…M-1
Question 2
Marks : +2 | -2
Pass Ratio : 50%
Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?
y(n)=\\(\\sum_{k=0}^{M+1} b_k x(n+k)\\)
y(n)=\\(\\sum_{k=0}^{M+1} b_k x(n-k)\\)
y(n)=\\(\\sum_{k=0}^{M-1} b_k x(n-k)\\)
None of the mentioned
Explanation:
An FIR filter of length M with input x(n) and output y(n) is described by the difference equation
Question 3
Marks : +2 | -2
Pass Ratio : 50%
If the unit sample response h(n) of the filter is real, complex valued roots need not occur in complex conjugate pairs.
True
False
Explanation:
We know that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z-1). This implies that if the unit sample response h(n) of the filter is real, complex valued roots must occur in complex conjugate pairs.
Question 4
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Pass Ratio : 50%
The roots of the equation H(z) must occur in ________________
Identical
Zero
Reciprocal pairs
Conjugate pairs
Explanation:
We know that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z-1). Consequently, the roots of H(z) must occur in reciprocal pairs.
Question 5
Marks : +2 | -2
Pass Ratio : 50%
The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.
True
False
Explanation:
We can express the output sequence as the convolution of the unit sample response h(n) of the system with the input signal. The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.
Question 6
Marks : +2 | -2
Pass Ratio : 50%
The roots of the polynomial H(z) are identical to the roots of the polynomial H(z-1).
True
False
Explanation:
We know that z-(M-1).H(z-1)=±H(z). This result implies that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z-1).
Question 7
Marks : +2 | -2
Pass Ratio : 50%
What is the value of h(M-1/2) if the unit sample response is anti-symmetric?
0
1
-1
None of the mentioned
Explanation:
When h(n)=-h(M-1-n), the unit sample response is anti-symmetric. For M odd, the center point of the anti-symmetric is n=M-1/2. Consequently, h(M-1/2)=0.
Question 8
Marks : +2 | -2
Pass Ratio : 50%
What is the number of filter coefficients that specify the frequency response for h(n) symmetric?
(M-1)/2 when M is odd and M/2 when M is even
(M-1)/2 when M is even and M/2 when M is odd
(M+1)/2 when M is even and M/2 when M is odd
(M+1)/2 when M is odd and M/2 when M is even
Explanation:
We know that, for a symmetric h(n), the number of filter coefficients that specify the frequency response is (M+1)/2 when M is odd and M/2 when M is even.
Question 9
Marks : +2 | -2
Pass Ratio : 50%
Which of the following condition should the unit sample response of a FIR filter satisfy to have a linear phase?
h(M-1-n) n=0,1,2…M-1
±h(M-1-n) n=0,1,2…M-1
-h(M-1-n) n=0,1,2…M-1
None of the mentioned
Explanation:
An FIR filter has an linear phase if its unit sample response satisfies the condition
Question 10
Marks : +2 | -2
Pass Ratio : 50%
What is the number of filter coefficients that specify the frequency response for h(n) anti-symmetric?
(M-1)/2 when M is even and M/2 when M is odd
(M-1)/2 when M is odd and M/2 when M is even
(M+1)/2 when M is even and M/2 when M is odd
(M+1)/2 when M is odd and M/2 when M is even
Explanation:
We know that, for a anti-symmetric h(n) h(M-1/2)=0 and thus the number of filter coefficients that specify the frequency response is (M-1)/2 when M is odd and M/2 when M is even.