Triangular Pulse

Define a triangular time pulse.

Figure 1. Define a triangular time pulse.

Time axis unit: Specify the unit to be used for the time axis.
Total signal duration ( $s_{d}$ $s_{d}$ ): The total length of the signal in the specified units.
Amplitude ( $u_{0}$ $u_{0}$ ): The amplitude of the time signal.
Pulse delay ( $t_{0}$ $t_{0}$ ): The pulse delay is the time until the peak of the time signal envelope.
Pulse width ( $p_{w}$ $p_{w}$ ): 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 ( $u_{0}$ $u_{0}$ ).
Rise time ( $τ_{1}$ $τ_{1}$ ): The time required for the pulse to reach its peak value ( $u_{0}$ $u_{0}$ ) from rest.
Fall time ( $τ_{2}$ $τ_{2}$ ): The time required for the pulse to reach the rest value from its peak ( $u_{0}$ $u_{0}$ ).
Note: The discharge time will be determined by the pulse width ( $p_{w}$ $p_{w}$ ).
Number of samples: The number of samples taken from the signal’s analytical equation.

(1)

u (t) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} u_{0} (1 - \frac{| t - t_{0} |}{p_{w}}) & for & | t - t_{0} | \leq p_{w} 0 & for & otherwise \end{matrix}

$u (t) = {\begin{array}{crl} u_{0} (1 - \frac{| t - t_{0} |}{p_{w}}) & for & | t - t_{0} | \leq p_{w} \\ 0 & for & otherwise \end{array}$

The Fourier transform is as follows:

(2)

U (f) = 2 u_{0} p_{w} {s i n c}^{2} (2 f p_{w}) e^{- j 2 π f t_{0}}

$U (f) = 2 u_{0} p_{w} {s i n c}^{2} (2 f p_{w}) e^{- j 2 π f t_{0}}$