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Lecture
Fourier Analysis: Fourier Series and Transform
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Discrete Fourier Transform: Introduction and Sampling
Covers the introduction of discrete Fourier transform and its implications on signal reconstruction.
Discrete Fourier Transform: Unlimited Duration Signals
Explores the Discrete Fourier Transform applied to signals of unlimited duration using various windows for improved accuracy.
Sampling and Reconstruction
Covers sampling, Fourier Transform, and reconstruction using low-pass filters in signal processing.
Fourier Transform: Basics and Applications
Covers the basics of the Fourier transform and its applications in signal processing.
Fourier Transforms: Properties and Applications
Explores Fourier transforms, including properties, convolution, Parseval's theorem, and energy spectral density for non-periodic functions.
Fourier transforms: Light-matter interaction
Explores Fourier and Laplace transforms in materials science, focusing on light-matter interaction, diffraction patterns, and crystal properties.
Discrete Fourier series: Inherent periodicities and time shifts
Explores the Discrete Fourier Transform synthesis and analysis formulas, time shifts for finite-length signals, and the equivalence between DFS and DFT.
Fourier Transform: Derivatives and Formulas
Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.
Fourier Analysis: Lecture Recap
Offers a recap of Fourier Analysis, focusing on key concepts and formulas.
Fourier Transform: Analysis IV
Covers the Fourier transform in Analysis IV, discussing Fourier series and solutions for various problems.
