This module reviews the main properties of the Shah function and addresses the interpolation problem. Key elements include:
This module introduces the Fourier series, emphasizing the significance of previous knowledge in Matlab. Students will explore periodic phenomena and understand the relationship between time and space. Key concepts include:
This module discusses how sine and cosine can model more complex functions. Students will learn about:
This module focuses on analyzing general periodic phenomena as sums of simple periodic phenomena. Key topics include:
This module wraps up the discussion on Fourier series, emphasizing the significance of infinite sums and convergence. Topics covered include:
This module continues the discussion of Fourier series and introduces the heat equation. Key concepts include:
This module corrects previous discussions on the heat equation and sets up the Fourier transform derivation from Fourier series. Key elements include:
This module reviews the definitions of the Fourier transform and its inverse, focusing on key properties. Topics include:
This module explores the effects of shifting a signal on its Fourier transform. Key concepts include:
This module continues the discussion of convolution, focusing on its formula and application in filtering. Key topics include:
This module covers the central limit theorem (CLT) and its relation to convolution. Key content includes:
This module introduces generalized functions and distributions. Important topics include:
This module sets up the Fourier transform of a distribution, discussing essential concepts such as:
This module covers the derivative of a distribution, including practical examples such as:
This module introduces the application of the Fourier transform in diffraction. Key components include:
This module continues the discussion on diffraction patterns and their relationship with the Fourier transform. Key topics include:
This module reviews the main properties of the Shah function and addresses the interpolation problem. Key elements include:
This module discusses sampling and interpolation results, addressing key concepts such as:
This module provides an aliasing demonstration using music and transitions to discrete signals. It includes:
This module reviews the definition of the discrete Fourier transform (DFT). Important topics include:
This module continues the review of basic definitions of the discrete Fourier transform (DFT). Key points include:
This module sets up the FFT algorithm through DFT matrix notation. Key topics include:
This module introduces basic definitions of linear systems. Key concepts discussed include:
This module reviews the previous lecture on discrete versus continuous linear systems. Key elements include:
This module continues the review of last lecture, emphasizing LTI systems and convolution. Key concepts include:
This module introduces the higher-dimensional Fourier transform. Key topics include:
This module reviews higher-dimensional Fourier transforms, focusing on separable functions. Important topics include:
This module covers the shift theorem in higher dimensions. Key components include:
This module delves into Shah functions, lattices, and their relevance to crystallography. Key topics include:
This module discusses tomography and the process of inverting the Radon transform. Key elements include: