Discrete transforms | Fourier analysis
In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample. A family of transforms composed of sine and sine hyperbolic functions exists. These transforms are made based on the natural vibration of thin square plates with different boundary conditions. The DST is related to the discrete cosine transform (DCT), which is equivalent to a DFT of real and even functions. See the DCT article for a general discussion of how the boundary conditions relate the various DCT and DST types. Generally, the DST is derived from the DCT by replacing the Neumann condition at x=0 with a Dirichlet condition. Both the DCT and the DST were described by Nasir Ahmed T. Natarajan and K.R. Rao in 1974. The type-I DST (DST-I) was later described by Anil K. Jain in 1976, and the type-II DST (DST-II) was then described by H.B. Kekra and J.K. Solanka in 1978. (Wikipedia).
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
Fourier Transforms: Discrete Fourier Transform, Part 2
Data Science for Biologists Fourier Transforms: Discrete Fourier Transform Part 2 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
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
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
Introduction to the z-Transform
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduces the definition of the z-transform, the complex plane, and the relationship between the z-transform and the discrete-time Fourier transfor
From playlist The z-Transform
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
Discrete Fourier Transform - Simple Step by Step
Easy explanation of the Fourier transform and the Discrete Fourier transform, which takes any signal measured in time and extracts the frequencies in that signal. This is a work in progress, let me know if anything doesn't make sense, and I will update the video to make that clearer. Tha
From playlist Fourier
Sine waves in time and in frequency
This video provides a deeper introduction to sine waves. This lecture plus the next lecture (dot-product) are essential for understanding how the Fourier transform works. The video uses files you can download from https://github.com/mikexcohen/ANTS_youtube_videos For more online courses
From playlist OLD ANTS #2) The discrete-time Fourier transform
Lecture: Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT)
This lecture details the algorithm used for constructing the FFT and DFT representations using efficient computation.
From playlist Beginning Scientific Computing
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
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
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
ME565 Lecture 16: Discrete Fourier Transforms (DFT)
ME565 Lecture 16 Engineering Mathematics at the University of Washington Discrete Fourier Transforms (DFT) Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L16.pdf Course Website: http://faculty.washington.edu/sbrunton/me565/ http://faculty.washington.edu/sbrunton/
From playlist Fourier
Lecture: Theory of the Fourier Transform
Outline of the basic theory of the Fourier Transform and the representation of data in the frequency domain
From playlist Beginning Scientific Computing
11: Spectral Analysis Part 1 - Intro to Neural Computation
MIT 9.40 Introduction to Neural Computation, Spring 2018 Instructor: Michale Fee View the complete course: https://ocw.mit.edu/9-40S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61I4aI5T6OaFfRK2gihjiMm Covers complex Fourier series, transforms, discrete Fourier tra
From playlist MIT 9.40 Introduction to Neural Computation, Spring 2018
Lecture 17, Interpolation | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 17, Interpolation 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
Lec 7 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 7: z-Transform properties 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
How MRI Works - Part 3 - Fourier Transform and K-Space
How MRI works, Part 3 - The Fourier Transform and k-Space Part 1: https://youtu.be/TQegSF4ZiIQ Part 2: https://youtu.be/M7yh0To6Wbs FFT code: https://github.com/thePIRL/fft-code-for-fun/blob/main/FFT%20code 0:00 - Intro 1:00 - The Sinusoid and phasors 5:48 - Fourier Theory 9:05 - The Fo
From playlist Summer of Math Exposition 2 videos