This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Design of FIR Filters”.

1. Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?

d) None of the mentioned

View Answer

Explanation: An FIR filter of length M with input x(n) and output y(n) is described by the difference equation

where {bk} is the set of filter coefficients.

2. The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.

a) True

b) False

View Answer

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.

3. Which of the following condition should the unit sample response of a FIR filter satisfy to have a linear phase?

a) h(M-1-n) n=0,1,2…M-1

b) ±h(M-1-n) n=0,1,2…M-1

c) -h(M-1-n) n=0,1,2…M-1

d) None of the mentioned

View Answer

Explanation: An FIR filter has an linear phase if its unit sample response satisfies the condition

h(n)= ±h(M-1-n) n=0,1,2…M-1.

4. If H(z) is the z-transform of the impulse response of an FIR filter, then which of the following relation is true?

View Answer

Explanation: We know that and h(n)= ±h(M-1-n) n=0,1,2…M-1

When we incorporate the symmetric and anti-symmetric conditions of the second equation into the first equation and by substituting z -1 for z, and multiply both sides of the resulting equation by z -(M-1) we get

5. The roots of the polynomial H(z) are identical to the roots of the polynomial H(z -1).

a) True

b) False

View Answer

Explanation: We know that . This result implies that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z -1).

6. The roots of the equation H(z) must occur in:

a) Identical

b) Zero

c) Reciprocal pairs

d) Conjugate pairs

View Answer

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.

7. If the unit sample response h(n) of the filter is real, complex valued roots need not occur in complex conjugate pairs.

a) True

b) False

View Answer

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.

8. What is the value of h(M-1/2) if the unit sample response is anti-symmetric?

a) 0

b) 1

c) -1

d) None of the mentioned

View Answer

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.

9. What is the number of filter coefficients that specify the frequency response for h(n) symmetric?

a) (M-1)/2 when M is odd and M/2 when M is even

b) (M-1)/2 when M is even and M/2 when M is odd

c) (M+1)/2 when M is even and M/2 when M is odd

d) (M+1)/2 when M is odd and M/2 when M is even

View Answer

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.

10. What is the number of filter coefficients that specify the frequency response for h(n) anti-symmetric?

a) (M-1)/2 when M is even and M/2 when M is odd

b) (M-1)/2 when M is odd and M/2 when M is even

c) (M+1)/2 when M is even and M/2 when M is odd

d) (M+1)/2 when M is odd and M/2 when M is even

View Answer

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.

11. Which of the following is not suitable either as low pass or a high pass filter?

a) h(n) symmetric and M odd

b) h(n) symmetric and M even

c) h(n) anti-symmetric and M odd

d) h(n) anti-symmetric and M even

View Answer

Explanation: If h(n)=-h(M-1-n) and M is odd, we get H(0)=0 and H(π)=0. Consequently, this is not suitable as either a low pass filter or a high pass filter.

12. The anti-symmetric condition with M even is not used in the design of which of the following linear-phase FIR filter?

a) Low pass

b) High pass

c) Band pass

d) Bans stop

View Answer

Explanation: When h(n)=-h(M-1-n) and M is even, we know that H(0)=0. Thus it is not used in the design of a low pass linear phase FIR filter.

13. The anti-symmetric condition is not used in the design of low pass linear phase FIR filter.

a) True

b) False

View Answer

Explanation: We know that if h(n)=-h(M-1-n) and M is odd, we get H(0)=0 and H(π)=0. Consequently, this is not suitable as either a low pass filter or a high pass filter and when h(n)=-h(M-1-n) and M is even, we know that H(0)=0. Thus it is not used in the design of a low pass linear phase FIR filter. Thus the anti-symmetric condition is not used in the design of low pass linear phase FIR filter.

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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