Gaussian Pulse (Normal Distribution)

Define a Gaussian time pulse with a normal distribution.



Figure 1. 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 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) u ( t ) = { 0 for  t t 0 u 0 ( e t t 0 τ 1 e t t 0 τ 2 ) for  t > t 0

The Fourier transform is as follows:

(2) U ( f ) = u 0 ( τ 1 1 + j 2 π f τ 1 τ 2 1 + j 2 π f τ 2 ) e j 2 π f t 0