Question: 21 -

What is the number of filter coefficients that specify the frequency response for h(n) symmetric?

(M-1)/2 when M is even and M/2 when M is odd

(M+1)/2 when M is odd and M/2 when M is even

(M-1)/2 when M is odd and M/2 when M is even

(M+1)/2 when M is even and M/2 when M is odd

Answer:

(M+1)/2 when M is odd and M/2 when M is even

Solution:

For a symmetric h(n), the number of filter coefficients that specify the frequency response is (M+1)/2 when M is odd and M/2 when M is even.

Question: 22 -

What is the approximate transition width of main lobe of a Hamming window?

12π/M

4π/M

8π/M

2π/M

Answer:

8π/M

Solution:

The transition width of the main lobe in the case of Hamming window is equal to 8π/M where M is the length of the window.

Question: 23 -

Which of the following is not suitable either as low pass or a high pass filter?

h(n) symmetric and M odd

h(n) symmetric and M even

h(n) anti-symmetric and M odd

h(n) anti-symmetric and M even

Answer:

h(n) anti-symmetric and M odd

Solution:

If h(n)=-h(M-1-n) and M is odd, we get H(0)=0 and H(π)=0. Consequently, this is not suitable as either a low pass filter or a high pass filter.

Question: 24 -

What is the value of h(M-1/2) if the unit sample response is anti-symmetric?

0

-1

None of these

1

Answer:

0

Solution:

When h(n)=-h(M-1-n), the unit sample response is anti-symmetric. For M odd, the center point of the anti-symmetric is n=M-1/2. Consequently, h(M-1/2)=0.

Question: 25 -

The anti-symmetric condition with M even is not used in the design of which of the following linear-phase FIR filter?

Low pass

Band stop

High pass

Band pass

Answer:

Low pass

Solution:

When h(n)=-h(M-1-n) and M is even, we know that H(0)=0. Thus it is not used in the design of a low pass linear phase FIR filter.