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
- Using L'Hopitals to evaluate the case. Note that n & m are integers
Notation
Linear Time Invariant Systems
Must meet the following criteria
- Time independance
- Linearity
- Superposition (additivity)
- Scaling (homogeneity)
Complex Conjugate
Changing Basis Functions
Identities