Uniqueness of Fourier Representations

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Fourier Analysis: Complex Coefficients and Series Properties

Explores Fourier analysis with complex coefficients and key series properties.

Fourier Analysis: Fourier Series and Transform

Explores Fourier series, DFT, FFT, and their applications in signal processing and spectroscopy.

Fourier Series: Dirichlet Theorem and Convergence

Explores Fourier series, Dirichlet theorem, and convergence properties in periodic functions.

Signals & Systems I: Fourier Transform and Dirac Pulse

Explores Fourier transformation, sign function, Dirac pulse, series development, and periodic signal synthesis.

Fourier Transform: Compression and Analysis

Covers the Fourier transform, compression techniques, and spectral analysis of periodic signals.

Convergence and Divergence of Series

Covers the definitions of convergent and divergent series and explores the harmonic series and alternating series.

Wave Propagation: General Solutions

Explores the general solutions for wave propagation and Fourier transforms in periodic functions.

Fourier Transform: Schwartz Space

Covers the Fourier transform on Schwartz space and its properties, including continuity and linearity, as well as the density of smooth compactly supported functions.

Fourier transforms: Light-matter interaction

Explores Fourier and Laplace transforms in materials science, focusing on light-matter interaction, diffraction patterns, and crystal properties.

Fourier Analysis: Inversion Formula

Explores the Fourier inversion formula and the importance of the integral on the half-circle being zero for the method to work.