# Double Exponential Piecewise Pulse

Define a double exponential piecewise time pulse.

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.
Charge duration ( ${c}_{d}$ )
The charge duration is the time from the pulse delay has ended until the signal begins to discharge.
Charge time constant ( ${\tau }_{2}$ )
The time that would be required to discharge the signal down to 36.8% of its full potential ( ${u}_{0}$ ).
Charge time constant ( ${\tau }_{1}$ )
The time that would be required to charge the signal up to 63.2% of its full potential ( ${u}_{0}$ ).
Number of samples
The number of samples taken from the signal’s analytical equation.
(1)
(2) ${u}_{1}=\frac{{u}_{0}}{1-{e}^{-\frac{{c}_{d}}{{\tau }_{1}}}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}{u}_{2}=\frac{{u}_{0}}{{e}^{-\frac{{c}_{d}}{{\tau }_{2}}}}$

The Fourier transform is as follows:

(3)