Fourier analysis

Discrete Fourier series

In digital signal processing, the term Discrete Fourier series (DFS) is any periodic discrete-time signal comprising harmonically-related (i.e. Fourier) discrete real sinusoids or discrete complex exponentials, combined by a weighted summation. A specific example is the inverse discrete Fourier transform (inverse DFT). (Wikipedia).

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The Two-Dimensional Discrete Fourier Transform

The two-dimensional discrete Fourier transform (DFT) is the natural extension of the one-dimensional DFT and describes two-dimensional signals like images as a weighted sum of two dimensional sinusoids. Two-dimensional sinusoids have a horizontal frequency component and a vertical frequen

From playlist Fourier

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Intro to Fourier series and how to calculate them

Download the free PDF from http://tinyurl.com/EngMathYT This is a basic introduction to Fourier series and how to calculate them. An example is presented that illustrates the computations involved. Such ideas are seen in university mathematics.

From playlist Fourier

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The Discrete Fourier Transform

This video provides a basic introduction to the very widely used and important discrete Fourier transform (DFT). The DFT describes discrete-time signals as a weighted sum of complex sinusoid building blocks and is used in applications such as GPS, MP3, JPEG, and WiFi.

From playlist Fourier

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How to compute a Fourier series: an example

Free ebook http://tinyurl.com/EngMathYT This video is a demonstration on how to compute a Fourier series of a simple given function. I discuss how to calculate the Fourier coefficients through integration and the simplifications involved. Fourier series are an important area of applied

From playlist Engineering Mathematics

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Discrete Fourier Transform - Introduction

An introduction to the Discrete Fourier Transform (DFT) and its interpretation.

From playlist Mathematical Physics II Uploads

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Intro to Fourier series & how to calculate them

Download the free PDF http://tinyurl.com/EngMathYT This is a basic introduction to Fourier series and how to calculate them. An example is presented that illustrates the computations involved. Such ideas are seen in university mathematics.

From playlist Several Variable Calculus / Vector Calculus

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Fourier Transforms: Discrete Fourier Transform, Part 3

Data Science for Biologists Fourier Transforms: Discrete Fourier Transform Part 3 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton

From playlist Fourier

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The Discrete Fourier Transform (DFT)

This video introduces the Discrete Fourier Transform (DFT), which is how to numerically compute the Fourier Transform on a computer. The DFT, along with its fast FFT implementation, is one of the most important algorithms of all time. Book Website: http://databookuw.com Book PDF: http

From playlist Fourier

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Discrete Fourier Transform - Example

We do a very simple example of a Discrete Fourier Transform by hand, just to get a feel for it. We quickly realize that using a computer for this is a good idea...

From playlist Mathematical Physics II Uploads

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Lec 8 | MIT RES.6-008 Digital Signal Processing, 1975

Lecture 8: The discrete Fourier series Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES6-008S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-008 Digital Signal Processing, 1975

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Lec 9 | MIT RES.6-008 Digital Signal Processing, 1975

Lecture 9: The discrete Fourier transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES6-008S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-008 Digital Signal Processing, 1975

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Lecture 10, Discrete-Time Fourier Series | MIT RES.6.007 Signals and Systems, Spring 2011

Lecture 10, Discrete-Time Fourier Series Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6.007 Signals and Systems, 1987

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Lecture 11, Discrete-Time Fourier Transform | MIT RES.6.007 Signals and Systems, Spring 2011

Lecture 11, Discrete-Time Fourier Transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6.007 Signals and Systems, 1987

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19. Relations Among Fourier Representations

MIT MIT 6.003 Signals and Systems, Fall 2011 View the complete course: http://ocw.mit.edu/6-003F11 Instructor: Dennis Freeman License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.003 Signals and Systems, Fall 2011

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The discrete-time Fourier transform

The Fourier transform is arguably the most important algorithm in signal processing and communications technology (not to mention neural time series data analysis!). This video provides an in-depth, step-by-step explanation of how the Fourier transform works. The video uses files you can

From playlist OLD ANTS #2) The discrete-time Fourier transform

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Fourier Transforms: Discrete Fourier Transform, Part 1

Data Science for Biologists Fourier Transforms: Discrete Fourier Transform Part 1 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton

From playlist Fourier

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Lec 31 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Lecture 31: Examples of discrete Fourier transform; fast Fourier transform; convolution (part 1) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008

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Math 139 Fourier Analysis Lecture 04: Uniqueness of Fourier Series

Uniqueness of Fourier Series: all Fourier coefficients vanish implies function vanishes at points of continuity; absolute convergence of Fourier series implies uniform convergence of Fourier series to the original (continuous) function; twice continuous differentiability implies absolute c

From playlist Course 8: Fourier Analysis

Related pages

Poisson summation formula | Periodic summation | Digital signal processing | Discrete-time Fourier transform