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Lecture
Fourier Inversion Formula and Plancherel Identity
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Fourier Inversion Formula
Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.
Trigonometric Polynomials: Fourier Inversion and Plancherel Formulas
Explores trigonometric polynomials, emphasizing Fourier inversion and Plancherel formulas.
Central Limit Theorem
Explores the Central Limit Theorem, convergence in law, characteristic functions, and moment problems in probability theory.
Convergence of Fourier Series
Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.
Fourier Series: Understanding Coefficients and Periodicity
Explores Fourier series coefficients, periodicity, and series relations.
Fourier Transform: Properties and Convolution
Covers the properties and convolution of the Fourier transform.
Fourier Transform: Properties and Applications
Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.
Fourier Transforms: Properties and Applications
Explores Fourier transforms, including properties, convolution, Parseval's theorem, and energy spectral density for non-periodic functions.
Signal Representations
Covers the properties of signal/data representations using Fourier transformations and matrices.
Solving unbounded PDE's using Fourier Transforms and Convolution: Obtaining the d'Alembert solution of the wave equation
Explores elementary properties of Fourier Transforms, convolution, Parseval's Theorem, and the d'Alembert solution of the wave equation using Fourier Transforms and convolution.