# Optimum Equi Ripple Filter Design

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Design of Optimum Equi Ripple Linear Phase FIR Filters-2”.

1. If δ1 represents the ripple in the pass band for a chebyshev filter, then which of the following conditions is true?
a) 1-δ1 ≤ Hr(ω) ≤ 1+δ1; |ω|≤ωP
b) 1+δ1 ≤ Hr(ω) ≤ 1-δ1; |ω|≥ωP
c) 1+δ1 ≤ Hr(ω) ≤ 1-δ1; |ω|≤ωP
d) 1-δ1 ≤ Hr(ω) ≤ 1+δ1; |ω|≥ωP

2. If the filter has symmetric unit sample response with M odd, then what is the value of Q(ω)?
a) cos(ω/2)
b) sin(ω/2)
c) 1
d) sinω

3. If the filter has anti-symmetric unit sample response with M odd, then what is the value of Q(ω)?
a) cos(ω/2)
b) sin(ω/2)
c) 1
d) sinω

4. In which of the following way the real valued desired frequency response is defined?
a) Unity in stop band and zero in pass band
b) Unity in both pass and stop bands
c) Unity in pass band and zero in stop band
d) Zero in both stop and pass band

5. The error function E(ω) should exhibit at least how many extremal frequencies in S?
a) L
b) L-1
c) L+1
d) L+2

6. The filter designs that contain maximum number of alternations are called as ______________
a) Extra ripple filters
b) Maximal ripple filters
c) Equi ripple filters
d) None of the mentioned

7. Remez exchange algorithm is an iterative algorithm used in error approximation.
a) True
b) False

8. When |E(ω)|≤δ for all frequencies on the dense set, the optimal solution has been found in terms of the polynomial H(ω).
a) True
b) False

9. In Parks-McClellan program, an array of maximum size 10 that specifies the weight function in each band is denoted by?
a) WTX
b) FX
c) EDGE
d) None of the mentioned

10. The filter designs which are formulated using chebyshev approximating problem have ripples in?
a) Pass band
b) Stop band
c) Pass & Stop band
d) Restart band

11. If the filter has symmetric unit sample response with M even, then what is the value of Q(ω)?
a) cos(ω/2)
b) sin(ω/2)
c) 1
d) sinω

12. Which of the following filter design is used in the formulation of design of optimum equi ripple linear phase FIR filter?
a) Butterworth approximation
b) Chebyshev approximation
c) Hamming approximation
d) None of the mentioned

13. If δ2 represents the ripple in the stop band for a chebyshev filter, then which of the following conditions is true?
a) 1-δ2 ≤ Hr(ω) ≤ 1+δ2;|ω|≤ωs
b) 1+δ2 ≤ Hr(ω) ≤ 1-δ2;|ω|≥ωs
c) δ2 ≤ Hr(ω) ≤ δ2;|ω|≤ωs
d) -δ2 ≤ Hr(ω) ≤ δ2;|ω|≥ωs

14. If the filter has anti-symmetric unit sample response with M even, then what is the value of Q(ω)?
a) cos(ω/2)
b) sin(ω/2)
c) 1
d) sinω

15. It is convenient to normalize W(ω) to unity in the stop band and set W(ω)=δ2/ δ1 in the pass band.
a) True
b) False

16. Which of the following defines the weighted approximation error?
a) W(ω)[Hdr(ω)+Hr(ω)]
b) W(ω)[Hdr(ω)-Hr(ω)]
c) W(ω)[Hr(ω)-Hdr(ω)]
d) None of the mentioned
.

17. The error function E(ω) does not alternate in sign between two successive extremal frequencies.
a) True
b) False

18. At most how many extremal frequencies can be there in the error function of ideal low pass filter?
a) L+1
b) L+2
c) L+3
d) L

19. The filter designs that contain more than L+2 alternations are called as ______________
a) Extra ripple filters
b) Maximal ripple filters
c) Equi ripple filters
d) None of the mentioned

20. If M is the length of the filter, then at how many number of points, the error function is computed?
a) 2M
b) 4M
c) 8M
d) 16M

21. If |E(ω)|<δ for some frequencies on the dense set, then a new set of frequencies corresponding to the L+2 largest peaks of |E(ω)| are selected and computation is repeated.
a) True
b) False

22. What is the value of JTYPE in the Parks-McClellan program for a Hilbert transformer?
a) 1
b) 2
c) 3
d) 4

23. In Parks-McClellan program, the grid density for interpolating the error function is denoted by which of the following functions?
a) NFILT
b) NBANDS
c) EDGE
d) LGRID

24. In Parks-McClellan program, an array of maximum size 10 that specifies the desired frequency response in each band is denoted by?
a) WTX
b) FX
c) EDGE
d) None of the mentioned