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What is the number of filter coefficients that specify the frequency response for h(n) anti-symmetric?
- a)(M-1)/2 when M is even and M/2 when M is odd
- b)(M-1)/2 when M is odd and M/2 when M is even
- 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 'B'. Can you explain this answer?
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Verified Answer
What is the number of filter coefficients that specify the frequency r...
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.
Most Upvoted Answer
What is the number of filter coefficients that specify the frequency r...
Answer:
To determine the number of filter coefficients that specify the frequency response for an anti-symmetric impulse response h(n), we need to consider the length of the impulse response and the symmetry properties.
Symmetry properties:
- An anti-symmetric sequence satisfies the property h(n) = -h(M-1-n), where M is the length of the sequence.
- In other words, the impulse response is symmetric about the midpoint of the sequence.
Determining the number of coefficients:
- When M is odd, the midpoint of the sequence is an integer (M-1)/2. In this case, the number of coefficients needed to specify the frequency response is M/2.
- When M is even, the midpoint of the sequence is a half-integer (M-1)/2. In this case, the number of coefficients needed to specify the frequency response is (M-1)/2.
Therefore, the correct answer is option 'B': (M-1)/2 when M is odd and M/2 when M is even.
Explanation:
- When the impulse response is anti-symmetric, it means that the frequency response will have odd symmetry. This means that the frequency response will have zeros at every odd multiple of the Nyquist frequency.
- The number of coefficients needed to specify the frequency response depends on the length of the impulse response and the symmetry properties.
- When the length of the impulse response is odd, the midpoint of the sequence is an integer. In this case, the frequency response will have (M/2) zeros.
- When the length of the impulse response is even, the midpoint of the sequence is a half-integer. In this case, the frequency response will have ((M-1)/2) zeros.
- By considering the symmetry properties and the length of the impulse response, we can determine the number of filter coefficients needed to specify the frequency response for an anti-symmetric impulse response.
To determine the number of filter coefficients that specify the frequency response for an anti-symmetric impulse response h(n), we need to consider the length of the impulse response and the symmetry properties.
Symmetry properties:
- An anti-symmetric sequence satisfies the property h(n) = -h(M-1-n), where M is the length of the sequence.
- In other words, the impulse response is symmetric about the midpoint of the sequence.
Determining the number of coefficients:
- When M is odd, the midpoint of the sequence is an integer (M-1)/2. In this case, the number of coefficients needed to specify the frequency response is M/2.
- When M is even, the midpoint of the sequence is a half-integer (M-1)/2. In this case, the number of coefficients needed to specify the frequency response is (M-1)/2.
Therefore, the correct answer is option 'B': (M-1)/2 when M is odd and M/2 when M is even.
Explanation:
- When the impulse response is anti-symmetric, it means that the frequency response will have odd symmetry. This means that the frequency response will have zeros at every odd multiple of the Nyquist frequency.
- The number of coefficients needed to specify the frequency response depends on the length of the impulse response and the symmetry properties.
- When the length of the impulse response is odd, the midpoint of the sequence is an integer. In this case, the frequency response will have (M/2) zeros.
- When the length of the impulse response is even, the midpoint of the sequence is a half-integer. In this case, the frequency response will have ((M-1)/2) zeros.
- By considering the symmetry properties and the length of the impulse response, we can determine the number of filter coefficients needed to specify the frequency response for an anti-symmetric impulse response.
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What is the number of filter coefficients that specify the frequency response for h(n) anti-symmetric?a)(M-1)/2 when M is even and M/2 when M is oddb)(M-1)/2 when M is odd and M/2 when M is evenc)(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 'B'. Can you explain this answer?
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