# Pulse Width and Duty cycle in Gaussian pulses

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?

• Mind sharing the source? I would like to see what the entire context is on how it's being modeled and used. I ask because it may require some modification of the pulse's expression to make more sense (at least to me). – Envidia Dec 3 '20 at 20:27