# Double Exponential Difference Pulse

Define a double exponential difference 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.
Time constant ( ${\tau }_{1}$ )
The pulse is defined as the difference of two exponentially charging pulses. The value of ${\tau }_{1}$ describes the time that would be required for the subtracted signal to reach 63.2% of its full potential ( ${u}_{0}$ ).
Time constant ( ${\tau }_{2}$ )
The value of ${\tau }_{2}$ describes the time that would be required for the base signal to reach 63.2% of its full potential ( ${u}_{0}$ ).
Number of samples
The number of samples taken from the signal’s analytical equation.
(1)

The Fourier transform is as follows:

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