Basic Continuous Time Signals

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function. These are collectively referred to as singularity functions.

Singularity functions are characterized by discontinuities or discontinuous derivatives.

The unit step function is zero for negative time values and one for positive time values, exhibiting a discontinuity at time zero.

This function often represents abrupt changes, as exemplified by the step voltage introduced on turning a car's ignition key.

The derivative of the unit step function yields the unit impulse function.

The unit impulse function is zero everywhere except at time zero, where it remains undefined.

It is a short-duration pulse with a unit area, signifying an applied or resulting shock.

Integrating a function with the impulse function yields the value of the function at the impulse point. This characteristic is called sampling.

Integrating the unit step function results in the unit ramp function. The unit ramp function is zero for negative time values and increases constantly for positive time values, representing a function that changes steadily.