The Fourier transform of text rect (t/tau) is X(f) = tau,text sinc (ftau). For tau = 1,text ms , the first spectral null occurs at:

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Electrical Engineering QUESTION #2171

Question 1

The Fourier transform of $\text{rect}(t/\tau)$ is $X(f) = \tau\,\text{sinc}(f\tau)$. For $\tau = 1\,\text{ms}$, the first spectral null occurs at:

Correct Answer Explanation

The first null of $\text{sinc}(f\tau)$ occurs at $f\tau = 1$, i.e., $f = 1/\tau = 1/10^{-3} = 1\,\text{kHz}$.