# FIR Filters Design

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)?
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

2. The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.
a) True
b) False

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

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) zM+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 roots of the equation H(z) must occur in ________________
a) Identical
b) Zero
c) Reciprocal pairs
d) Conjugate 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

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

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

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

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. 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

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