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What is the number of filter coefficients that specify the frequency response for h(n) symmetric?
- a)(M-1)/2 when M is odd and M/2 when M is even
- b)(M-1)/2 when M is even and M/2 when M is odd
- c)(M+1)/2 when M is even and M/2 when M is odd
- d)(M+1)/2 when M is odd and M/2 when M is even
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
What is the number of filter coefficients that specify the frequency r...
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.
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Community Answer
What is the number of filter coefficients that specify the frequency r...
Explanation:
Symmetric Filter Coefficients:
- In a symmetric filter, the coefficients are symmetric around the center point.
- For an odd-length filter (M is odd), the center coefficient is at index M/2.
- For an even-length filter (M is even), the center point is between two coefficients at indices M/2 and M/2 + 1.
Number of Coefficients for Frequency Response:
- For a symmetric filter, the number of coefficients required to specify the frequency response depends on the length of the filter.
Option D:
- The correct answer, option D, states that when M is odd, the number of coefficients needed is (M+1)/2.
- When M is even, the number of coefficients required is M/2.
Explanation of Option D:
- Consider the case where M is odd. The center coefficient is at index M/2. There are (M+1)/2 coefficients to the left of the center and (M+1)/2 coefficients to the right, totaling M+1 coefficients.
- In the case of an even M, the center point is between two coefficients at indices M/2 and M/2 + 1. There are M/2 coefficients on either side of the center, totaling M coefficients.
Therefore, option D correctly represents the number of filter coefficients needed to specify the frequency response for a symmetric filter.
Symmetric Filter Coefficients:
- In a symmetric filter, the coefficients are symmetric around the center point.
- For an odd-length filter (M is odd), the center coefficient is at index M/2.
- For an even-length filter (M is even), the center point is between two coefficients at indices M/2 and M/2 + 1.
Number of Coefficients for Frequency Response:
- For a symmetric filter, the number of coefficients required to specify the frequency response depends on the length of the filter.
Option D:
- The correct answer, option D, states that when M is odd, the number of coefficients needed is (M+1)/2.
- When M is even, the number of coefficients required is M/2.
Explanation of Option D:
- Consider the case where M is odd. The center coefficient is at index M/2. There are (M+1)/2 coefficients to the left of the center and (M+1)/2 coefficients to the right, totaling M+1 coefficients.
- In the case of an even M, the center point is between two coefficients at indices M/2 and M/2 + 1. There are M/2 coefficients on either side of the center, totaling M coefficients.
Therefore, option D correctly represents the number of filter coefficients needed to specify the frequency response for a symmetric filter.
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What is the number of filter coefficients that specify the frequency response for h(n) symmetric?a)(M-1)/2 when M is odd and M/2 when M is evenb)(M-1)/2 when M is even and M/2 when M is oddc)(M+1)/2 when M is even and M/2 when M is oddd)(M+1)/2 when M is odd and M/2 when M is evenCorrect answer is option 'D'. Can you explain this answer?
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