Fundamentals

Periodic Functions

Fundamental Frequency

Harmonics

Orthogonality

Trigonometric Fourier Series

Series Formula

Coefficient Formulas

Symmetry Properties (Parity)

Half-range Expansions

Complex Fourier Series

Series Formula

Complex Coefficients

Relation to Trigonometric Coefficients

Magnitude

Properties

Linearity

Time Shifting

Time Scaling

Differentiation Property

Convolution (Periodic and Discrete)

Analysis Tools

Parseval’s Equality

Power of Harmonics

RMS Value

Distance Between Functions

Convergence (Dirichlet Conditions)

Gibbs Phenomenon

Discrete Transforms (DFT)

DFT Formula

FFT Algorithm

Handwritten