Fourier Transformation: Fundamentals

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Explores the Fourier transformation, Parseval relation, weak convergence, and generalized transformations in signals and systems.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers matrix operations, Fourier transformations, Gaussian models, and signal representations using algebraic methods.

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Discusses mutual information, data processing inequality, and properties related to leakage in discrete systems.

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Covers the concept of distributions with compact support and their interpolation spaces.

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Covers the concepts of compression and prediction using prefix-free codes and distributions.

Covers probability distributions, moments, and continuous random variables.