# Digital Signal Processing Questions and Answers – Design of Optimum Equi Ripple Linear Phase FIR Filters – 1

This set of Digital Signal Processing online test focuses on “Design of Optimum Equi Ripple Linear Phase FIR Filters-1”.

1. 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

Explanation: The filter design method described in the design of optimum equi ripple linear phase FIR filters is formulated as a chebyshev approximation problem.

2. 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

Explanation: Let us consider the design of a low pass filter with the stop band edge frequency ωs and the ripple in the stop band is δ2, then from the general specifications of the chebyshev filter, in the stop band the filter frequency response should satisfy the condition
2 ≤ Hr(ω) ≤ δ2;|ω|≥ωs

3. 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

Explanation: If the filter has a anti-symmetric unit sample response, then we know that
h(n)= -h(M-1-n)
and for M even in this case, Q(ω)=sin(ω/2).

4. 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

Explanation: The weighting function on the approximation error allows to choose the relative size of the errors in the different frequency bands. In particular, it is convenient to normalize W(ω) to unity in the stop band and set W(ω)=δ21 in the pass band.

5. 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

Explanation: The weighted approximation error is defined as E(ω) which is given as
E(ω)=W(ω)[Hdr(ω)- Hr(ω)].
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6. The error function E(ω) does not alternate in sign between two successive extremal frequencies.
a) True
b) False

Explanation: The error function E(ω) alternates in sign between two successive extremal frequency, Hence the theorem is called as Alternative theorem.

7. 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

Explanation: We know that we can have at most L-1 local maxima and minima in the open interval 0<ω<π. In addition, ω=0 and π are also usually extrema. It is also maximum at ω for pass band and stop band frequencies. Thus the error function of a low pass filter has at most L+3 extremal frequencies.

8. 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

Explanation: In general, the filter designs that contain more than L+2 alternations or ripples are called as Extra ripple filters.

9. 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

Explanation: Having the solution for P(ω), we can now compute the error function E(ω) from
E(ω)=W(ω)[Hdr(ω)-Hr(ω)] on a dense set of frequency points. Usually, a number of points equal to 16M, where M is the length of the filter.

10. 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

Explanation: 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.

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

Explanation: The value of JTYPE=3 in the Parks-McClellan program to select a filter that performs Hilbert transformer.

12. 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

Explanation: In Parks-McClellan program, LGRID represents the grid density for interpolating the error function. The default value is 16 if left unspecified.

13. 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

Explanation: FX denotes an array of maximum size 10 that specifies the desired frequency response in each band.

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