# The Fourier Transforms and Its Applications

## Video Lectures

Displaying all 30 video lectures.

Lecture 1Play Video |
OverviewLecture 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 2Play Video |
Analyzing General Periodic PhenomenonLecture 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 3Play Video |
Analysis of Periodic PhenomenaLecture 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 4Play Video |
Heat FlowLecture 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 5Play Video |
Periodic Phenomena to Non Periodic PhenomenaLecture 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 6Play Video |
Fourier TransformsLecture 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 7Play Video |
Fourier Properties and TransformsLecture 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 8Play Video |
Fourier Combinations and FunctionsLecture 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 9Play Video |
ConvolutionLecture 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 10Play Video |
Central Limit TheoremLecture 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 11Play Video |
Confronting the Convergence of IntervalsLecture 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 12Play Video |
Fourier FunctionsLecture 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 13Play Video |
Fourier Transforms of a General DistributionLecture 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 14Play Video |
Fourier DistributionsLecture 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 15Play Video |
Properties of DeltasLecture 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 16Play Video |
Fourier Transforms and Its ApplicationsLecture 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 17Play Video |
InterpolationLecture 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 18Play Video |
Phenomena associated with InterpolationLecture 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 19Play Video |
AliasingLecture 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 20Play Video |
Discrete Fourier TransformLecture 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 21Play Video |
Properties of Discrete Fourier transformsLecture 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 22Play Video |
Fast Fourier Transform AlgorithmLecture 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 23Play Video |
Linear time and variance SystemsLecture 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 24Play Video |
Linear SystemsLecture 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 25Play Video |
Lecture 25: Fourier Transforms and its ApplicationsLecture 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 26Play Video |
Linear time-invariant System TheoryLecture 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 27Play Video |
Higher DimensionsLecture 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 28Play Video |
Higher Dimensional Fourier TransformsLecture 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 29Play Video |
Stretch TheoremLecture 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 30Play Video |
TomographyLecture 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. |