Elementary Signals

There are 5 different types of elementary functions: '''unit step function, rectangular function, ramp function, triangular function, and impulse function. '''

The unit step function and the impulse function are considered to be fundamental functions in engineering, and it is strongly recommended that the reader becomes very familiar with both of these functions.

Unit step function
Unit step function is like flipping switch on or off. If t>0 then switch will on, if t<0 will be off. Ku(t), K is constant and is use in ramp function. The unit step function, also known as the Heaviside function. Sometimes, u(0) is given other values, usually either 0 or 1. For many applications, it is irrelevant what the value at zero is. u(0) is generally written as undefined.

Youtube video: Unit step function

Rectangular function
Youtube video: Rectangular function Rectangular function is a little more complex than unit step function. We could say it is combine of two unit step function. But more importantly there is a theta that we add in to the function as new unknown.( Theta is on the time axis)

Ramp function
Youtube video: Ramp function Ramp function is the slope function that uses the Kr(t) the constant to determine the angle of the slope.

Triangular function
Advance version of ramp function is the triangular function. This is when the T(t) of the a |T| is absolute value there for it looks like triangular function.

Impulse function(Delta function)
An impulse function is a special function is to model certain events. Impulse function is not realizable, the out put of the impulse function is usually infinity at certain values.

The one on the right is rectangular function change to impulse function.

The delta piece wises function has some properties which included.

Most important property of impulse function is sifting Property it effectively samples the value of the function f, at location A and this is use to sample continuous function into discrete values.Using this property, we can extract a single value from a continuous function by multiplying with an impulse, and then integrating.

Youtube video : Impulse function

Problems
Combine with signal operations

Problem

Solution

Extra Resources
MIT open course