I have a pulse-based radar which transmits frequency-shifted Gaussian pulses. The Gaussian pulse ($p(t)$) is given by:
$$ p(t) = V_\text{TX} e^{\frac{-t^2}{2 \tau ^2}}. $$
The frequency shifted Gaussian pulse (g(t)) is given by:
\begin{align} g(t) &= p(t)\cos(\omega_{c}t)\\ &= V_\text{TX} e^{\frac{-t^2}{2 \tau ^2}}\cos(\omega_{c}t). \end{align}
where $\omega_{c}$ is the carrier frequency in rad/s.
How do we define the pulse width of this specific pulse, and also how is the duty cycle defined in this pulse?
