# FIR Filters Design MCQ’s

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

1. 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

2. 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

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

a) y(n)=∑M+1k=0bkx(n+k)

b) y(n)=∑M+1k=0bkx(n−k)

c) y(n)=∑M−1k=0bkx(n−k)

d) None of the mentioned

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

a) z^{M+1}.H(z^{-1})=±H(z)

b) z^{-(M+1)}.H(z^{-1})=±H(z)

c) z^{(M-1)}.H(z^{-1})=±H(z)

d) z^{-(M-1)}.H(z^{-1})=±H(z)

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

a) True

b) False

6. 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

7. The roots of the equation H(z) must occur in ________________

a) Identical

b) Zero

c) Reciprocal pairs

d) Conjugate pairs

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

a) True

b) False

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

a) True

b) False

10. 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

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

12. 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

13. 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

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