Signals	Systems	System Response
Frequency Representation	Fourier Series / Transforms	Background Material

Properties or theorems involving Dirac delta function

- Sampling theorem

Continuous

Discrete

How is this used?

             Ex.   Solve the integral.

- Integral of Dirac delta function

The unit step function is a unique function that is zero up until t = 0, then becomes one until +∞.

Derivative of Unit Step Function

Let us define Euler's formula as:

We can then define a transformation from polar coordinates to rectangular coordinates as:

The reverse transformation can also be defined:

Most importantly, we need a way to define complex operations. Thus, let us define an x where

and a y where

Then, we can define addition and subtraction where the real terms add together and the imaginary terms add together.

For multiplication, it is most important to note that when two imaginary numbers multiply, the solution is real because . After multiplication, we also group the real terms with the real terms and the imaginary terms with the imaginary terms.

For division, it is most important to remember to multiply the numerator and denominator by the complex conjugate of the denominator. This way we can make the denominator entirely real.