# Design of Optimum Equi Ripple Linear Phase FIR Filter MCQ [Free PDF] – Objective Question Answer for Design of Optimum Equi Ripple Linear Phase FIR Filter Quiz

1. Which of the following filter design is used in the formulation of the design of optimum equi ripple linear phase FIR filter?

A. Butterworth approximation
B. Chebyshev approximation
C. Hamming approximation
D. None of the mentioned

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

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

3. If the filter has an 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

If the filter has an 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 stopband and set W(ω)=δ2/ δ1 in the passband.

A. True
B. False

The weighting function on the approximation error allows to choose of the relative size of the errors in the different frequency bands. In particular, it is convenient to normalize W(ω) to unity in the stopband and set W(ω)=δ2/δ1 in the passband.

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

The weighted approximation error is defined as E(ω) which is given as
E(ω)=W(ω)[Hdr(ω)- Hr(ω)].

6. The error function E(ω) does not alternate in sign between two successive extremal frequencies.

A. True
B. False

The error function E(ω) alternates in sign between two successive extremal frequencies, Hence the theorem is called an Alternative theorem.

7. At most how many extremal frequencies can be there in the error function of the ideal low pass filter?

A. L+1
B. L+2
C. L+3
D. L

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 stopband 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

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

9. If M is the length of the filter, then at how many the number of points, the error function is computed?

A. 2M
B. 4M
C. 8M
D. 16M

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