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Bandwidth of the gate function is __________

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in Signals and Systems by (1.2m points)
Bandwidth of the gate function is __________

(a) τ  Hz

(b) \(\frac{1}{τ}\)  Hz

(c) 2τ Hz

(d) \(\frac{2}{τ}\)  Hz

The question was posed to me in an online quiz.

This intriguing question comes from Fourier Transforms in division Fourier Transform of Signals and Systems

1 Answer

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by (42.1k points)
The correct choice is (b) \(\frac{1}{τ}\)  Hz

Best explanation: The practical bandwidth of the gate function corresponds to the first zero crossing in the spectrum. Therefore, the bandwidth of the pulse or gate function is \(\frac{2π}{τ}\) or \(\frac{1}{τ}\) Hz.

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