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What is the magnitude response |W(ω)| of a rectangular window function?
a) |sin(ωM/2)||sin(ω/2)| b) |sin(ω/2)||sin(ωM/2)|
c) |cos(ωM/2)||sin(ω/2)| d) None of the mentioned?
a) |sin(ωM/2)||sin(ω/2)| b) |sin(ω/2)||sin(ωM/2)|
c) |cos(ωM/2)||sin(ω/2)| d) None of the mentioned?
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What is the magnitude response |W(ω)| of a rectangular window function...
Rectangular Window Function Magnitude Response:
The magnitude response |W(ω)| of a rectangular window function is given by:
Answer: b) |sin(ω/2)| * |sin(ωM/2)|
Explanation:
Rectangular Window Function:
- A rectangular window function is defined as W(ω) = 1 for |ω| ≤ π/M and W(ω) = 0 for |ω| > π/M, where M is the window length.
Magnitude Response:
- The magnitude response |W(ω)| is the absolute value of the Fourier transform of the window function.
- The Fourier transform of a rectangular window function is given by sinc functions, i.e., sin(ω/2)/ω.
- Therefore, the magnitude response |W(ω)| can be expressed as |sin(ω/2)| * |sin(ωM/2)|.
Conclusion:
- The correct magnitude response of a rectangular window function is |sin(ω/2)| * |sin(ωM/2)|, which represents the frequency response of the window function.
The magnitude response |W(ω)| of a rectangular window function is given by:
Answer: b) |sin(ω/2)| * |sin(ωM/2)|
Explanation:
Rectangular Window Function:
- A rectangular window function is defined as W(ω) = 1 for |ω| ≤ π/M and W(ω) = 0 for |ω| > π/M, where M is the window length.
Magnitude Response:
- The magnitude response |W(ω)| is the absolute value of the Fourier transform of the window function.
- The Fourier transform of a rectangular window function is given by sinc functions, i.e., sin(ω/2)/ω.
- Therefore, the magnitude response |W(ω)| can be expressed as |sin(ω/2)| * |sin(ωM/2)|.
Conclusion:
- The correct magnitude response of a rectangular window function is |sin(ω/2)| * |sin(ωM/2)|, which represents the frequency response of the window function.
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What is the magnitude response |W(ω)| of a rectangular window function? a) |sin(ωM/2)||sin(ω/2)| b) |sin(ω/2)||sin(ωM/2)| c) |cos(ωM/2)||sin(ω/2)| d) None of the mentioned?
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