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QUESTION: 1

The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.

Solution:

Explanation: We can express the output sequence as the convolution of the unit sample response h(n) of the system with the input signal. The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.

QUESTION: 2

Which of the following condition should the unit sample response of a FIR filter satisfy to have a linear phase?

Solution:

Explanation: An FIR filter has an linear phase if its unit sample response satisfies the condition

h(n)= ±h(M-1-n) n=0,1,2…M-1.

QUESTION: 3

The roots of the equation H(z) must occur in:

Solution:

Explanation: We know that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z -1). Consequently, the roots of H(z) must occur in reciprocal pairs.

QUESTION: 4

If the unit sample response h(n) of the filter is real, complex valued roots need not occur in complex conjugate pairs.

Solution:

Explanation: We know that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z -1). This implies that if the unit sample response h(n) of the filter is real, complex valued roots must occur in complex conjugate pairs.

QUESTION: 5

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

Solution:

Explanation: 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: 6

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

Solution:

Explanation: We know that, 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: 7

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

Solution:

Explanation: We know that, for a anti-symmetric h(n) h(M-1/2)=0 and thus 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: 8

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

Solution:

Explanation: 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: 9

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

Solution:

Explanation: 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.

QUESTION: 10

The anti-symmetric condition is not used in the design of low pass linear phase FIR filter.

Solution:

Explanation: We know that 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 and 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. Thus the anti-symmetric condition is not used in the design of low pass linear phase FIR filter.

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