List I (Signal) | List II (Fourier Transform) | ||
|---|---|---|---|
| A | $ x(t-t_0)$ | I | $ \frac{dx(\omega)}{{d\omega}}$ |
| B | $ e^{j \omega_0 t} x(t) $ | II | $ e^{j \omega t_0} X(\omega) $ |
| C | $ \frac{dx(t)}{{dt}}$ | III | $ x(\omega-\omega_0)$ |
| D | $(-jt)x(t) $ | IV | $j\omega X(\omega) $ |
Let \( X(\omega) \) be the Fourier transform of the signal
\( x(t) = e^{-4t}\cos(t), \; -\infty < t < \infty \).
The value of the derivative of \( X(\omega) \) at \( \omega = 0 \) is _____________
(rounded off to 1 decimal place).