Fourier series - by Ray Betz

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Fourier Series

If

  1. Dirichlet conditions are satisfied

then we can write

The above equation is called the complex fourier series. Given , we may determine by taking the inner product of with . Let us assume a solution for of the form . Now we take the inner product of with .

If then,

If then,

We can simplify the above two conclusion into one equation.

So, we may conclude

Orthogonal Functions

The function and are orthogonal on if and only if .

The set of functions are orthonormal if and only if .

Linear Systems