The Fourier Transforms and Its Applications

Video Lectures

Displaying all 30 video lectures.
Lecture 1
Overview
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Overview
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood provides an overview of the course, then begins lecturing on Fourier series.
Lecture 2
Analyzing General Periodic Phenomenon
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Analyzing General Periodic Phenomenon
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood's lecture addresses the question- How can we use such simple functions, sin(t) and cos(t) to model such periodic phenomenon? He takes the students through the first steps in analyzing general periodic phenomenon.
Lecture 3
Analysis of Periodic Phenomena
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Analysis of Periodic Phenomena
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues lecturing on the analysis of periodic phenomena and how it is represented.
Lecture 4
Heat Flow
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Heat Flow
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood wraps up the theoretical aspects of the Fourier Series, an application to heat flow.
Lecture 5
Periodic Phenomena to Non Periodic Phenomena
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Periodic Phenomena to Non Periodic Phenomena
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood finishes up on Fourier series, then he talks about the transformation Fourier series compared to the Fourier Transformations and how one gets to the study of periodic phenomena to non periodic phenomena by means of a limiting process.
Lecture 6
Fourier Transforms
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Fourier Transforms
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood picks up where he left off last lecture on Fourier Transformations, then he launches into a more formal treatment of Fourier transforms and explains how to proceed.
Lecture 7
Fourier Properties and Transforms
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Fourier Properties and Transforms
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood reintroduces the Fourier Transform and its inverse, then he goes into specific properties and transforms.
Lecture 8
Fourier Combinations and Functions
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Fourier Combinations and Functions
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues lecturing on the general properties of the Fourier Transforms by two paths. First, to develop specific transforms and second, to understand the Fourier transforms with different combinations and functions.
Lecture 9
Convolution
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Convolution
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on convolution and recaps on Fourier transformations and signal combinations.
Lecture 10
Central Limit Theorem
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Central Limit Theorem
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood introduces the final operation of convolution to the central limit theorem.
Lecture 11
Confronting the Convergence of Intervals
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Confronting the Convergence of Intervals
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on confronting the convergence of intervals.
Lecture 12
Fourier Functions
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Fourier Functions
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood reminds the students that the best class of functions for Fourier Functions are rapidly decreasing functions.
Lecture 13
Fourier Transforms of a General Distribution
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Fourier Transforms of a General Distribution
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). In this lecture, Professor Osgood demonstrates Fourier transforms of a general distribution.
Lecture 14
Fourier Distributions
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Fourier Distributions
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on distributions.
Lecture 15
Properties of Deltas
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Properties of Deltas
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood introduces a new application of the Fourier Transforms that includes deltas, properties of deltas, and physical interpretation of deltas.
Lecture 16
Fourier Transforms and Its Applications
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Fourier Transforms and Its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on diffraction and connects it to his next topic, sampling and interpolation.























The Fourier transform is a tool for solving physical problems. In this course the emphasis is on relating the theoretical principles to solving practical engineering and science problems.
Lecture 17
Interpolation
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Interpolation
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood begins his lecture on sampling and interpolation and discusses the associated properties.
Lecture 18
Phenomena associated with Interpolation
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Phenomena associated with Interpolation
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues the lecture on sampling and interpolation while discussing some of the phenomenon associated with it.
Lecture 19
Aliasing
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Aliasing
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood demonstrates aliasing by showing the class what happens when you under sample music.
Lecture 20
Discrete Fourier Transform
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Discrete Fourier Transform
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on the Discrete Fourier Transform.
Lecture 21
Properties of Discrete Fourier transforms
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Properties of Discrete Fourier transforms
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on the properties of discrete Fourier transforms.
Lecture 22
Fast Fourier Transform Algorithm
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Fast Fourier Transform Algorithm
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on the basics of the fast Fourier transform algorithm.
Lecture 23
Linear time and variance Systems
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Linear time and variance Systems
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on linear systems, focusing on linear time and variance systems.
Lecture 24
Linear Systems
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Linear Systems
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on linear systems.
Lecture 25
Lecture 25: Fourier Transforms and its Applications
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Lecture 25: Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on the relationship between LTI and the Fourier transforms.



The Fourier transform is a tool for solving physical problems. In this course the emphasis is on relating the theoretical principles to solving practical engineering and science problems.
Lecture 26
Linear time-invariant System Theory
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Linear time-invariant System Theory
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on the relationship between LTI and the Fourier transforms.
Lecture 27
Higher Dimensions
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Higher Dimensions
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his discussion on higher dimensions and the outer reaches while helping the students understand higher dimensions Fourier Transforms.
Lecture 28
Higher Dimensional Fourier Transforms
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Higher Dimensional Fourier Transforms
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the higher dimensional Fourier Transforms.
Lecture 29
Stretch Theorem
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Stretch Theorem
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the general stretch theorem and begins covering medical imaging.
Lecture 30
Tomography
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Tomography
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood's last lecture of the quarter, he finishes lecturing on tomography and inverting the radon transform in medical imaging.