Rectangular and Triangular Pulse Function

The unit rectangular pulse function is mathematically represented by the rectangular function centered at the origin with a height of one unit.

Two parameters define this function: T, specifying the center location of the pulse along the time axis, and τ, determining the pulse duration.

An example can be a rectangular pulse with a 5V amplitude, a 3s duration and a center located at time equals 2s. This pulse can be expressed using the rectangular function.

Synthesizing the rectangular pulse involves the graphical demonstration of sequentially adding two time-shifted step functions.

In general terms, a unit rectangular function can always be expressed using the unit step function.

The unit triangular function is mathematically expressed via the triangular function. It has unit height and is centered at the origin.

An instance is a triangular pulse centered at a time equal to 3s, with a magnitude of 2 and a width of 2s. To sketch a triangular pulse, replace every t with t-3 and set the width equal to two. The defined signal is demonstrated graphically.