Fourier Analysis
Signal Processing, Orthogonality, and Reciprocity
Orthogonality on the Circle
The geometric foundation of why sine and cosine can span a function space.
Odd & Even Representations
How function symmetry simplifies Fourier coefficients and aids computational efficiency.
Parseval's Identity
Energy conservation between time and frequency domains; a cornerstone of signal analysis.
The Poisson Kernel
A derivation of the cornerstone function for solving the Dirichlet problem on the disk.
Series Convergence Tests
Practical tools for determining the behavior of infinite trigonometric sums.