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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?
Verified 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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Most Upvoted Answer
What is the number of filter coefficients that specify the frequency r...
Explanation:

Filter Coefficients for Symmetric h(n):
- For a symmetric impulse response h(n), the filter coefficients are symmetric around the center coefficient.
- The symmetry property implies that half of the filter coefficients are redundant because they are mirror images of the other half.
- The number of unique coefficients needed to specify the frequency response is therefore less than the total number of coefficients.

Formula for Number of Filter Coefficients:
- When M is odd, the total number of coefficients is M, and the number of unique coefficients needed is (M+1)/2.
- When M is even, the total number of coefficients is M, and the number of unique coefficients needed is M/2.

Correct Answer Justification:
- The correct option D states that for h(n) symmetric, the number of filter coefficients needed is (M+1)/2 when M is odd and M/2 when M is even.
- This aligns with the explanation provided above and correctly identifies the number of unique coefficients required to specify the frequency response for a symmetric impulse response.
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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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