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Lecture
Fourier Transform: Definition and Properties
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Fourier Series and Transforms: Introduction and Properties
Covers Fourier series, Fourier transforms, and convolution properties, including linearity and commutativity.
Frequency Response of LTI Systems
Explores LTI systems, impulse response, convolution, system properties, and frequency response, including low-pass and band-pass filters.
Self Similar Solutions and Stokes Second Problem
Explores self-similar solutions, Fourier transform, Laplace transform, and Gaussian error function.
Image Processing in Frequency Space
Explores Fourier Transform, frequency filtering, segmentation, and particle size estimation using image analysis techniques.
Linear Time Invariant Systems
Covers LTI systems, impulse response, convolution, Fourier Transform, and system characterization.
Numerical Methods: Boundary Value Problems
Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.
Harmonic Analysis: Schwerte Functions
Explores Schwerte functions in harmonic analysis, emphasizing compact support and function convergence.
Fourier Transform: Concepts and Applications
Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.
Discrete-Time Fourier Transform
Introduces the discrete-time Fourier transform and its application to stable LTI systems, covering properties and frequency response.
Fourier Transform: Inversion Formula
Explores the Fourier Transform inversion formula and its applications in signal processing.
