COMBINATIONS OF CONTINUOUS TIME FUNCTIONS

Continuous Time Unit Impulse Applied at the Origin

The Continuous Time Unit Pulse applied at the origin is represented by δ(t). It is defined as:

It is graphically represented as:

(1) in the graphic indicates the area of the unit impulse.

Continuous Time Unit Step Applied at the Origin

The Continuous Time Unit Step applied at the origin is represented by u_-1(t). It is defined as:

It is graphically represented as:

The function is discontinuous at the origin.

Continuous Time Unit Ramp Applied at the Origin

The Continuous Time Unit Ramp applied at the origin is represented by u_-2(t). It is defined as:

It is graphically represented as:

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COMBINATIONS OF CONTINUOUS TIME FUNCTIONS

THE THREE FUNCTIONS

Three continuous time functions are used is Signals & Systems, Control Systems, Electric Circuits and other related areas. They are:

Continuous Time Unit Impulse Applied at the Origin

In case you do not remember the function definition, click on the magnifying glass.

Continuous Time Unit Step Applied at the Origin

In case you do not remember the function definition, click on the magnifying glass.

Continuous Time Unit Ramp Applied at the Origin

In case you do not remember the function definition, click on the magnifying glass.

The three functions can be combined to generate new ones. The resulting functions can make it easier to perform some computations.

The object presents a tool to compute new functions using the three that were defined. The following section introduces the syntax for the combinations to be performed.