Signals and systems/GF Fourier

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Fourier series

The Fourier series is used to analyze arbitrary periodic functions by showing them as a composite of sines and cosines.

A function is considered periodic if for .

The exponential form of the Fourier series is defined as

Determining the coefficient

The definition of the Fourier series

Integrating both sides for one period. The range of integration is arbitrary, but using scales nicely when extending the Fourier series to a non-periodic function

Multiply by the complex conjugate

Notation

Linear Time Invariant Systems

Changing Basis Functions

Identities