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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 ( sd )
The total length of the signal in the specified units.
Amplitude ( u0 )
The amplitude of the time signal.
Pulse delay ( t0 )
The pulse delay is the time until the peak of the time signal envelope.
Pulse width ( pw )
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 ( u0 ).
Number of samples
The number of samples taken from the signal’s analytical equation.
(1) u(t)={0for tt0u0(ett0τ1ett0τ2)for t>t0

The Fourier transform is as follows:

(2) U(f)=u0(τ11+j2πfτ1τ21+j2πfτ2)ej2πft0