# Gaussian Pulse (Normal Distribution)

Define a Gaussian time pulse with a normal distribution.

Time axis unit
Specify the unit to be used for the time axis.
Total signal duration ( ${s}_{\text{d}}$ )
The total length of the signal in the specified units.
Amplitude ( ${u}_{0}$ )
The amplitude of the time signal.
Pulse delay ( ${t}_{0}$ )
The pulse delay is the time until the peak of the time signal envelope.
Pulse width ( ${p}_{w}$ )
This is the half-amplitude pulse width of the signal. The pulse width is the total length of time that the signal is above 50% of its peak value ( ${u}_{0}$ ).
Number of samples
The number of samples taken from the signal’s analytical equation.
(1)

The Fourier transform is as follows:

(2) $\mathrm{U}\left(f\right)={u}_{0}\left(\frac{{\tau }_{1}}{1+j2\pi f{\tau }_{1}}-\frac{{\tau }_{2}}{1+j2\pi f{\tau }_{2}}\right){e}^{-j2\pi f{t}_{0}}$