Integral transforms

K-transform

In mathematics, the K transform (also called the Kemp-Macdonald Transform or Single-Pixel X-ray Transform) is an integral transform introduced by and in 2016. The transform allows a 3-dimensional inhomogeneous object to be reconstructed from scalar point measurements taken in the volume external to the object. Gunther Uhlmann proved that the K transform exhibits global uniqueness on , meaning that different objects will always have a different K transform. This uniqueness arises by the use of a monotonic, nonlinear transform of the X-ray transform. By selecting the exponential function for the transform function, which coincides with attenuation of particles in matter in accordance with the Beer–Lambert law, the K transform can be used to perform tomography of 3-dimensional objects using a low-resolution single-pixel detector. A numerical inversion using the BFGS optimization algorithm was explored by Fichtlscherer. (Wikipedia).

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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

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Electrical Engineering: Ch 19: Fourier Transform (2 of 45) What is a Fourier Transform? Math Def

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the mathematical definition and equation of a Fourier transform. Next video in this series can be seen at: https://youtu.be/yl6RtWp7y4k

From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM

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Electrical Engineering: Ch 19: Fourier Transform (1 of 45) What is a Fourier Transform?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a Fourier transform and how is it different from the Fourier series. Next video in this series can be seen at: https://youtu.be/fMHk6_1ZYEA

From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM

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The Fourier Transform and Derivatives

This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow

From playlist Fourier

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Fourier Transform

What is a Fourier Transform and how does it relate to the Fourier Series? In this video, we discuss the idea of the Fourier Cosine Transform.

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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Lecture 16 | The 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

From playlist Lecture Collection | The Fourier Transforms and Its Applications

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Lec 18 | MIT RES.6-008 Digital Signal Processing, 1975

Lecture 18: Computation of the discrete Fourier transform, part 1 Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES.6-008 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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Linear Algebra 8.1 General Linear Transformations

My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.

From playlist Linear Algebra

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Lecture 20 | The 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 the Discrete Fourier Transform. The Fourier transform is a tool for solving physical problems. In this course the emph

From playlist Lecture Collection | The Fourier Transforms and Its Applications

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Wavelets And Multiresolution Analysis Part 1

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From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math

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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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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

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Rec 13 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Recitation 13 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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Inversion of the z-Transform: Power Series Expansion

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Finding inverse z-tranforms by writing the z-transform as a power series expansion. Includes long division and inverting transcendental functions.

From playlist The z-Transform

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Let's Learn Physics: Fun with Fourier Transforms

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From playlist Let's Learn (Classical) Physics: ZAP Physics Livestreams

Related pages

One-time pad | Mathematics | Integral transform | Exponential function | Broyden–Fletcher–Goldfarb–Shanno algorithm | X-ray transform