Fourier Series Approximation

Fourier Transformation is a function f(t) derived from a given function and representing it by a series of sinusoidal functions. It is expressed as:

where,

It is used in multiple fields like signal and noise estimation, seismographs, and filtering.

To show how it works, we'll give the Fourier series of the given functions:

Since both of these functions is at t(0), we need to shift the charging formula.

If plotted, it will result to this:

Note that which equation Q(t) to use depends on time t,

To solve a0,

To solve an,

To solve bn,

By plugging the values, we will have f(t) as,

As we increase the approximation term n , the series approximation improves as well.